Radioactivity in the Marine Environment (1971)

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96 Radioactivity in the Marine Environment Temperature, °C FIGURE 3 Vertical temperature distribu- tion at a series of stations along a meridian in the Atlantic Ocean. (Reprinted with per- mission from Defant, 1961.) Je p 4 t u o 4 • 12 ii 0 4 ] a 0 | 4 | » 12 1« 20 24 •<l I l> I I J/ I I I I I I I JJ 1 - Ship Position Date 1. WillScoreby 554 63° 20' S 17° 23' W 5.ii. 1931 2. Meteor 58 48° 30' S 30° 0'W 7/8. x. 1925 3. Meteor 83 32° 9'S 25° 4'W 29. xi. 1925 4. Meteor 1 70 22° 39' S 27° 55' W 9. vii. 1926 5. Meteor 191 9° 7'S 2° 2'W 9/10. ix. 26 6. Meteor 212 0° 36' N 29° 12' W 19. x. 1926 7. Meteor 283 17°53'N 39° 19' W 22/23. iii. 1927 8. Dana 1376 33° 42' N 36° 16' W 10. vi. 1922 9. Armauer Hansen 17 58° 0'N 11° 0'W 29. vii. 1913 10. Fram 20 78° 1' N 9° 10' E 22. vii. 1910 J495SO 246 S.%, 340 2468 34,4 8 8 350 2 4 6 8 360 2 ] 4 ] « . 340 2467 I 340 2 I 4 C 8 I 344 6 6 390 2 4 6 * MO 2 FIGURE 4 Vertical salinity curves for a series of oceanographic stations along a me- ridional section through the Atlantic (see legend of Figure 3); corresponding vertical temperature curves are shown in Figure 3. (Reprinted with permission from Defant, 1961.)

Physical Processes of Water Movement and Mixing 97 1 sooo 70*S «0° 50° 4O° 3O" 20° IO°S O"N IO° Z0° S0» 40° 5O° «O°N FIGURE 5 Vertical sections showing dis- tributions of temperature, salinity, and oxy- gen in the western Atlantic Ocean. (Re- printed with permission from VVtist, 1935.) 7O°S 60° 5O* 4O° 30° 20° 10° 5 & M 10° 20° 30° 40 • 50° «O°N The salinity profiles at middle and tropical latitudes show more complicated structure above 1,500 m. A dominant feature in the South Atlantic is the salinity minimum at depths between 800 and 1,200 m, which has its origin in the Antarctic Convergence zone, at about 50°S. Figures 5 and 6 show vertical cross-sections of tempera- ture, salinity, and dissolved oxygen (in units of ml per liter) for the Atlantic and Pacific, respectively. These cross-sections extend from the Antarctic continent (on the left) nearly to the Arctic Circle. Figure 5, for the Atlantic, shows very clearly the northward intrusion of Antarctic intermediate water, with its core at a depth of roughly 1,000 m; this water is characterized by its relatively low temperature, low salinity, and high dissolved oxygen content. The apparent source of this water is at the surface near 50°S (the Antarc- tic Convergence zone). The oxygen section for the Atlantic shows a southward intrusion of high oxygen content with a core at about 3,000-m depth, which has its source in the North Atlantic between 50° and 60°N. Sverdrup et al. (1942) give evidence for a region of winter sinking in an area just south of Greenland (the Irminger Sea), which they pro- posed as a primary source of deep water in the North Atlan- tic. Figure 6, for the Pacific, does not indicate any similar source region. The temperature sections for both the Atlantic and Paci- fic suggest a northward intrusion, at the bottom, of cold water that apparently originates at the surface near the Ant- arctic continent with the onset of freezing during the south- ern winter. The northward intrusion of the Antarctic bottom water into the Atlantic is shown very clearly in a chart of temperature at 4,000 m, presented in a paper by Stommel (1955). Figure 7 is a cross-section of density for the Atlantic Ocean. The values indicated on the contours represent den- sity anomaly (in mg/ml), neglecting the influence of pres- sure. The value 27.0 corresponds to 1.0270 g/ml for a sample at 1 atm but at the in situ temperature and salinity. Except at great depth, the values of the density anomaly must increase with depth for gravitational stability of the water column. Hence, there is a noticeable absence of core structure, such as that indicated in the diagrams of Figure 5. The most stable water is located near the equator; the least stable water is in the northern latitudes, particularly during the winter season for the hemisphere concerned. Clearly, it

98 Radioactivity in the Marine Environment CARNtQIt FIGURE 6 Vertical sections showing dis- tribution of temperature, salinity, and oxy- gen in the Pacific Ocean, approximately along 170°W. (Reprinted with permission from Sverdruper al., 1942.) C<»Nt»1t * »USHNtLL 70°S eo° 50°40° SO* tO° J0° 50° 60° N 1000 2000 3000 4000 5000 FIGURE 7 Vertical density section along the western trough of the Atlantic, corresponding to temperature-salinity sections of Figure 5. (Reprinted with permission from Defant, 1961.)

99

100 Radioactivity in the Marine Environment is in the latter regions that excess cooling can result in verti- cal convection and provide the source for the deep and bot- tom water renewal. Complete renewal of the Common Water has been estimated by Bolin and Stommel (1961) to require on the average about 1,200 years. This can be compared to Montgomery's (1959) estimate of 10 years for the residence time of the surface mixed layers of the world ocean and to Bolin and Stommel's estimate of from 100 to 400 years residence time for the Atlantic Intermediate Water. For more detailed information about the distribution of properties, the reader may consult the works of Wiist (1935, 1949), Defant (1961), Fuglister (1960, 1963), Reid (1965), and others. The paper by Reid presents a very complete and up-to-date analysis of the properties of the Pacific Ocean. Surface and Near-Surface Currents Figure 8 shows the general features of the mean surface cur- rent pattern of the world ocean. More detailed charts show- ing magnitudes are published by the U.S. Navy Oceano- graphic Office. Although such currents as the Gulf Stream and Kuroshio are semipermanent, they change in strength and configuration from month to month (cf. Stommel, 1957; Warren, 1963; Fuglister, 1963). The most striking, but perhaps least studied, variable current regime is that of the northern and equatorial part of the Indian Ocean, the varia- tions being strongly coupled with the pronounced seasonal changes of the wind pattern (monsoons). Magnitudes of the quasipermanent currents (i.e., non- tidal currents) generally do not exceed about 250 cm/sec (5 knots). Values of this magnitude have been reported for the core of the Gulf Stream and Florida Current. More fre- quently, the stronger of the major current systems at the surface flow at less than 200 cm/sec. However, the lateral width of strong currents like the Gulf Stream is generally less than 100 km (the distance over which speeds exceed 10 percent of the core strength). Consequently, in the major area of the ocean surface, away from these "rivers of the sea," one finds typical speeds of 0 to 30 cm/sec, values that are comparable to the magnitude of tidal currents in the open sea. The depth of the northward-flowing Gulf Stream is about 1,000 to 1,500 m, depending upon location, and its speed decreases with increasing depth (Stommel, 1957). This is in marked contrast to the depth of the major equatorial cur- rent systems (less than about 500 m). Indeed, the surface Equatorial Current, which flows toward the west in all three oceans, is now known to be a superficial feature, lim- ited to perhaps a few decameters in depth. Hidden beneath this surface current, in all three oceans, lies the major, jet- like Equatorial Undercurrent, with speeds up to 150 cm/sec in its core and extending to depths of 400 to 500 m (cf. Knauss, 1960;Knauss and Taft, 1964;Metcalf et al, 1962; Knauss, 1966;Cochrane, 1963;Stalcup andMetcalf, 1966). The Equatorial Undercurrent of the Pacific has its core at the equator and is confined to the narrow band between about 1°N and 1°S. It has been traced as a well-defined sub- surface stream from the Gilbert Islands, at 174°E, to the Galapagos Islands, at 92°W. The total transport has been estimated to be about 40 million m3/sec (greater than that of the Florida Current, which is 26 million m3/sec).* The volume transports in the upper 1,000 m of the North Atlantic as estimated by Sverdrup et al. (1942) are indicated in Figure 9. The values for the Gulf Stream are now known to be somewhat low, the maximum transport off Cape Hat- teras being closer to 80 sv than to 55 sv. Moreover, the amount of water sinking in the Subarctic Convergence region near Greenland has been estimated by Stommel and Arons (1960b) to be more nearly 20 sv instead of 4 sv. The latter value is only a rough estimate. Observational evidence for deep currents certainly supports the idea that Sverdrup's initial estimate of 4 sv for the North Atlantic rate of supply to the deep water is too small. If this is true, then the com- pensational flow northward across the equator from the South Atlantic must be proportionately greater than indi- cated in Figure 9. Nevertheless, the figure does display the major qualitative features of the flow in the upper 1,000 m. The Antarctic Circumpolar Current is unique in that it represents the only current system on earth that is nearly a continuous zonal current circling the entire globe. This sys- tem is much deeper than 1,000 m, except in the region of the Drake Passage, between South America and the Antarc- tic continent. Its average total transport has been estimated to be in excess of 100 sv (Sverdrup et al., 1942). However, this figure is quite uncertain in the light of arguments ad- vanced by Stommel and Arons (1960b). In any event, the qualitative features of the flow as presented by Sverdrup (Figure 10) are probably valid. Intermediate and Deep Circulation The currents at a depth of 800 m as estimated from the field of density, using the geostrophic balance relation, are shown for the Atlantic Ocean in Figure 11. These estimates are based on a level of no motion, which is taken to be con- sistent with the spreading of the Antarctic Intermediate Water. Figure 11 indicates current directions substantially similar to those of the surface flow, except off the coast of Argentina. The speeds are generally less than 30 cm/sec. *For convenience in dealing with volume transports by currents, we will define a transport of 1 million m3/sec as a sverdrup (abbreviated sv). For example, the average volumetric rate of exchange of water between the Mediterranean Sea and the Atlantic is about 1.7 sv.

Physical Processes of Water Movement and Mixing 101 FIGURE 9 Transport of Central Water and Subarctic Water in the Atlantic Ocean. The lines with arrows indicate the direction of the transport, and the inserted numbers in- dicate the transported volumes in millions of cubic meters per second. Full-drawn lines show warm currents; dashed lines show cold currents. Areas of positive temperature anomaly are shaded. (Reprinted with per- mission from Sverdrupet al., 1942.) FIGURE 10 Transport lines around the Antarctic Continent. Between two lines, transport relative to the 3,000-decibar sur- face is about 20 million n*'/seC. (Reprinted with permission from Sverdrup et al., 1942.) Defant (1961) also estimated the currents at 2,000-m depth in the Atlantic based on the same reference level. The resulting picture of flow at this depth, as shown in Figure 12, is in striking contrast to those of flow at the surface (Figure 8) and at a depth of 800 m (Figure 11), particularly in the North Atlantic. At 2,000 m, a southward flow exists beneath the Gulf Stream and also along the coast of South America to 25°S, and current speeds are generally less than 20 cm/sec. Although some question exists concerning Defant's selec- tion of a spatially variable level of no motion, the fact re- mains that his picture of flow is strikingly similar to that predicted by Stommel and Arons (1960a, b), based on theo- retical grounds. (We will return to this point later.) Further

102 Radioactivity in the Marine Environment 60° 40* 10* 0' 20* 100° 80° 60° 40° 20° 0° 20° 40° r-"l1 nnd -» <3cmAec *^^ 9-12cm.Aec ^^^*»18-2 800m. —»6-9cm/jec •^l2-l8cm.Aec ^^*^ >24cmA«c FIGURE 11 Current field at a depth of 800 m, computed from the absolute topography of the 800-decibar surface. (Reprinted with permission from Defant, 1961.) 80* 60' 40° go* Q' 20° 20° 40' 100° 80° 60° 40° 20° 0° 20° 40 C 1 Lond -• «3cnv/j€C 2000m. — 3-6cm./sec l2-l8cm./»c FIGURE 12 Current field at a depth of 2,000 m, computed from the absolute topography of the 2,000-decibar surface. (Reprinted with permission from Defant, 1961.) support for the southward set of the deep currents along the western boundary of the North Atlantic is provided by the direct observations of Swallow and Worthington (1961), Volkmann (1962), and others. Table 3 is a reproduction of the results of deep current measurements in the region at or near 33°N, 75°W made by Swallow and Worthington with neutrally buoyant floats. The mean current indicated by these measurements, for the layer between 1,500 and 3,000 m, is about 8 cm/sec in a compass direction of 210°. Since the combined duration of these measurements is about 27 days, the tidal "noise" is essentially eliminated. How- ever, the variability from one measurement to another is still considerable (a range of 18 cm/sec). Stommel (1963) and Longuet-Higgins (1965) have suggested that such vari- ability might be attributed to planetary wave noise asso- ciated with the inherent variability of the atmospheric driving processes (primarily the stress of the winds). Some notion of the three-dimensional structure of circu- lation in the Atlantic Ocean is provided in a schematic dia- gram constructed by Wust (1949), which is reproduced in Figure 13. (Note that this figure shows north latitudes on the left and south on the right, in contrast to previous figures.) Theoretical Aspects In the central oceanic regime at mid-latitudes, away from the equator and the intense western boundary currents, the flow is characterized by very small Rossby number and small Reynolds number (based on the horizontal eddy viscosity).* *The Rossby number is fluid speed divided by a characteristic veloc- ity associated with the earth's rotation, which may be taken as rf where r is the mean radius of the earth and / is the local vertical component of the earth's vorticity (Coriolis parameter). Specifi- cally,/ = 2fl sin 1f, where fl is the earth's angular speed and , is the latitude. The Reynolds number is VplKh, where V is the fluid speed and Kh is the horizontal eddy viscosity associated with lateral turbulent mixing processes.

Physical Processes of Water Movement and Mixing 103 TABLE 3 Summary of Deep Current Measurements with Neutrally Buoyant Floats, March-April 1957, near 33°N, 75°W" Launched Last Fix Mean Observed Depth ±SD Mean Velocity ±SD (m) (cm/sec) Float Time Date Time Date °T±SD B 1000 6 0743 11 2,040 ± 70 0.33 t 0.11 108 ± 18 D 1715 17 0718 22 2.5506 ± 40 4.27 1.88 ± ± 0.21 0.11 201 ± 235 ± 1.4 4 F. 1527 20 1717 22 1,480 ± S0 6.42 6.50 + i 0.47 0.29 308 ± 4.7 2.3 231 ± F 0954 23 0733 25 2,620" ± 80 8.99 ± 0.53 190 ± 2.3 G 2050 23 1032 26 2,600* ± S0 4.41 7.08 ± ± 0.26 0.44 218 ± 203 ± 3.3 2.3 H 0815 26 0605 29 2,910c ± 70 18.36 ± 0.28 182 ± 1.0 I 0854 26 1040 29 2,760c ± 190 6.02 12.62 £ ± 0.27 0.39 216 ± 196 ± 2.6 1.3 J 1110 30 1103 2 2,900c ± 120 10.24 9.42 ± ± 0.18 0.22 204 ± 185 ± 1.7 11 K 1156 30 0935 31 2,770c ± 200 12.95 ± 0.59 207 ± 5.2 "Reprinted with permission from Swallow and Worthington, 1961. 6Mean for D, F, and G = 2,580 m. cMean for H, I, J, and K = 2,840 m. It can be shown (Stommel, 1957) that, under these condi- tions, the balance of torques on a fluid column extending from level z to the surface, under steady state conditions, is given approximately by the relation 0 ... f y 1 udz = fw +1 — J \9x 0) Here, x,y, and z represent local cartesian coordinates in the eastward, northward, and upward directions, respectively. The term/is the Coriolis parameter defined in the footnote, and 0 is the derivative of/in the y direction. The eastward and northward velocity components are denoted by u and v, and the vertical by w, at level z in equation (1). Finally, TX and Ty represent the eastward and northward components of wind stress at the surface (nominally at z = 0). It is as- sumed that the level z is taken below the depth of frictional influence (Ekman layer), which may extend to depths of about 100 or 200m. The physical interpretation of relation (1) is as follows: The term in parentheses is a wind stress torque per unit area; the term/w is the vorticity tendency term associated with stretching or shrinking of the water column; and the term on the left is the planetary vorticity tendency term, which is associated with displacement of the water column to a different latitude. If z is taken at the variable elevation of the seabed [z = -D(x,y)], then/w leads to a topographical influence that can be pronounced near the continental slopes (Warren, 1963). In the central abyssal region, in which the seabed is re- garded as horizontal, w must vanish at the bottom and Eq. (1) reduces to (2) for a column extending to the seabed. This is Sverdrup's approximation (1947); from it, one can calculate the merid- ional volume transport resulting from the wind-stress field as derived from climatological information. Using the conti- nuity equation for the column, 0 II 9 r a r — udz + —• vdz = 0, 9x J dy J -D -D (3) one can also evaluate the zonal component of volume trans- port, taking the latter as zero on the eastern boundary. In order to satisfy continuity on the western boundary of the ocean, we require a narrow frictional or inertial boundary current (Munk, 1950;Charney, 1955; Stommel, 1957). In the western boundary current regime, either lateral friction or inertial terms must be introduced into Eq. (2); indeed,

104 Radioactivity in the Marine Environment & K^ <*t /yt Ju'ij.tf *° *x>!fA.'oe£/lo°*t,o''l/ -$Wr fo/tf/s 6000 60°N 50° 40° 30° 20° 10° 0° 10° 20° 30° 40° 50° 60° 70°S 80 AD Antarctic Divergence sc Subtropical Convergence P Polarfront Physical seasurface level Boundary (~9°C) between warm water and cold water sphere Dynamical eference level ( layer of no motion ) Isohalines ^T*• Currents - - Vertical convection >34 8 S%o <348S%o / Cold water upwelling Velocities in depth:2,4,7 17 cm/sec (Geostroph1c components) Exaggeration of depth ~ I300X FIGURE 1 3 Schematic block-diagram of the surface currents, of salinity distribution, and of the deep sea circulation of the Atlantic Ocean. (After Wiist, 1949, corrected.) these effects dominate over the wind torque term in the boundary current regime. Relations (2) and (3) are valid in the central oceanic re- gime only for the total column of fluid (and even then only if the seabed is horizontal or if there is negligible motion at the bottom). These relations tell nothing about the internal vertical circulation or about differences of circulation in the upper and lower layers of the sea individually. In order to examine the transports in a layer from the surface to, say, 1,000-m depth (z = -1,000 m), one must use Eq. (1) with w evaluated at that depth. On the other hand, for the layer from 1,000 m to the mean sea floor (-4,000 m), the relation -1,000 0 I vdz = -fw -4,000 (4) is employed such that the sum of Eqs. (1) and (4) is consis- tent with Eq. (2). Moreover, the continuity relation for the upper 1,000 m is o o 9 f A 3 f — udz + — dx J by } vdz = w. (5) -1,000 -1,000

Physical Processes of Water Movement and Mixing 105 NORTH (s 20 ' 2 2« , f !" t 2 . n t 4 *U- J -T 4_± ) I 2 / P A 2 f 5 4 -*— J -»- J • ' V* 2 f t ' " '* 'J |-1 ,, J * R+Z8 B+J2 R •US — R+22 FIGURE 14 Schematic budget of transports below the 1,000-m depth in various portions of the world oceans. Numbers represent transports in units of 10" m-'/sec (sv). (Reprinted with permission from Stommel and Arons, 1960b.) The relations (1), (4), and (5) can be useful only if the vertical velocity, w, can be determined independently of these relations. The estimation of w for the steady state oceanic convection regime has been examined theoretically by Robinson and Stommel (1959) and later by Robinson and Welander (1963) and others. Robinson and Stommel found that a vertical (turbulent) exchange coefficient of about 0.7 cm2/sec leads to a realistic temperature profile for mid-latitude conditions. Moreover, they found an asso- ciated upward vertical velocity, typical of mid-latitudes, of about 10~5 cm/sec (about 1 cm/day). This upward motion is required in order to balance the downward diffusion of heat. In a later paper, by Stommel and Arons (1960b), the above thermohaline theory is employed to estimate the total upward transport from the deep water of the world ocean to the upper 1,000 m of the ocean. A value of about 40 sv is obtained. This upward transport must be balanced by sinking in the deep and intermediate water source re- gions (in the North Atlantic and the Antarctic region). They estimate that half of this sinking (20 sv) occurs in the North Atlantic near Greenland. Using Eqs. (1), (4), and (5) and an assumed uniform up- welling rate through the permanent thermocline of the world ocean, Stommel and Arons were able to obtain crude estimates of the deep-water transports within the westward boundary currents of the Atlantic, Indian, and Pacific oceans. With the exception of the Antarctic Circumpolar Current, they were also able to estimate the circulation within the deep water of the North Atlantic, the South Atlantic, and other areas. The results are shown schemati- cally in Figure 14. The directions and amounts of the trans- port between various segments of the schematic deep ocean -9 -10' -11 -lt -1 -2 -» 50' •>'?' 30' 20' LATITUDE SO' 40' LAT1TUDE FIGURE 15 Streamlines for the total mass transport in a northern hemisphere ocean, in the vertical meridional plane, based on the numerical model of Bryan and Cox (1967): (a) no wind; (b) mod- erate zonal wind; and (c) strong zonal wind. (Reprinted with per- mission from Bryan and Cox, 1967.) are indicated (R being an unknown deep-water transport around the Antarctic continent). In the theory presented by Stommel and Arons, it is im- plied that the major current in deep water occurs on the western boundary. However, it must be borne in mind that their theory deals with an ocean of uniform depth. In the Atlantic, the Mid-Atlantic Ridge represents a formidable barrier to the deep currents, and indeed the deep-water flow pattern obtained by Defant (Figure 12) shows a strong deep current with southward set just east of the Mid-Atlantic Ridge. Defant's pattern is supported by a more recent analy-

106 Radioactivity in the Marine Environment sis by Lappo (1963) that makes use of direct observations together with the observed density field. Serious efforts have recently been directed toward the problem of numerical modeling of the ocean circulation (Bryan, 1963; Gormatyuk and Sarkisyan, 1965; Holland, 1966; Bryan and Cox, 1967). The most comprehensive of these models is that of Bryan and Cox, which employs the complete set of hydrodynamic equations and the thermal diffusion-advection equation. They carried out a parametric study of the numerical model for different Rossby numbers, Reynolds numbers, and relative wind strengths. The primary deficiency of their present model (presumably for the North Atlantic) is that there is no allowance for the important interchange with the southern oceans across the equator. Figure 15 shows a plot of the steady-state, zonally averaged streamlines in a vertical section from 10°N to about 65°N as calculated by Bryan and Cox. The strength of the vertical circulation is changed only slightly by the wind; the govern- ing factor in controlling overturning is the impressed merid- ional temperature distribution at the sea surface. The total upward transport for the average of these re- sults is about 38 sv, based on realistic conditions for the parameters as stipulated by Bryan and Cox. This is about twice the estimate of Stommel and Arons (1960b) for the North Atlantic and nearly the same as the estimated total upwelling for the world ocean as a whole. Apparently, the reason for this excess overturn rate is that although the model is confined to a basin whose size and surface tempera- ture distribution are similar to those of the North Atlantic, no allowance has been made for interchange with the re- maining 8/9 of the world ocean. Accordingly, the estimated residence time in deep water of only about 100 years, im- plied by the Bryan and Cox model, is probably low by a factor of nine. Aside from this limitation of the present application of the model, the numerical technique does offer considerable potential with respect to the analysis of the distribution of contaminant introduced into the sea. continuous source. To understand these problems, we must acquire fairly precise knowledge of the physical processes of movement and dispersion of material due to oceanic cur- rents and turbulence rather than general knowledge of the overall rates of exchange, as in a "box model." Movement and diffusion of a radioactive material re- leased into the sea may be classified, according to the con- ditions under which it is released, as follows: instantaneous source, continuous fixed source, or continuous moving source. The intensity of the continuous fixed and continu- ous moving sources may vary with time, and each may be regarded as either infinitesimal or finite in size, depending upon the scale of diffusion. In the theory of diffusion or conduction in solids, the solution for an instantaneous point-source is regarded as fundamental (Carslaw and Jaeger, 1959). Thus, by integrat- ing the fundamental solution with respect to time with an appropriate source intensity, we obtain the solution for the continuous fixed point-source. By integrating with respect to appropriate space variables, we obtain solutions for in- stantaneous finite-sized sources. Solutions of a large number of other important problems can be obtained immediately from the fundamental solution. Such a fundamental solu- tion, in a rigorous sense, does not exist for the diffusion problem for a turbulent field: knowledge of the concentra- tion distribution for an instantaneous point-source is not sufficient to obtain the distribution of substance from a continuous point-source fixed in a turbulent field. In diffu- sion of the continuous point-source type, we must not only take into consideration diffusion relative to the centers of mass of individual elementary patches,* but we must also consider variabilities in the location of these centers of mass. In practical problems, however, we may approximate, in our calculations, the concentration from a continuous fixed point-source simply by superimposing an infinite number of diffusing patches from an instantaneous source, all of which are assumed to move at a single mean velocity. More will be said about this approach later. MIXING PROCESSES IN THE MARINE ENVIRONMENT In addition to local, continuous, extremely low-level sources, such as the processed liquid effluent from a shore- based nuclear installation, artificially produced radioactivity might also be introduced into the sea through local instan- taneous release, such as might result from an accident to a seaborne or airborne nuclear power source, for example. In such releases, fairly local problems will be important, such as the maximum concentration in a patch of radioactivity after a known interval of time, or the concentration along the centerline of a plume of radioactivity released from a Instantaneous Releases The horizontal scale of turbulence in the sea is usually so much greater than the vertical scale that, for many purposes, their effects on diffusion can be considered separately. Revelle et al. (1956) cited an example of diffusion of radio- active material released below the thermocline; the material spread over an area of 100 km2 while its vertical extent did not exceed 1 m. Similarly, Folsom and Vine (1957) de- scribed the horizontal spread of radioactive tracer over an *Which may be considered as being of the instantaneous point-source type.

Physical Processes of Water Movement and Mixing 107 area of 40,000 km2 in 40 days while it remained in a surface layer less than 60 m deep. These experimental facts seem to indicate that the hori- zontal components of oceanic turbulence play an essential role in the horizontal spread of material introduced into the marine environment. A method of approach to the oceanic diffusion problem suggested by this finding has been used by various investigators. In this approach we first assume that the substance is subject to horizontal diffusion within a sufficiently thin homogeneous layer that all vertical varia- tions in concentration may be ignored. We further assume that it is possible to describe the distribution, after some time has elapsed, with lines of equal concentration. In other words, we treat the problem as if the diffusion took place on a purely two-dimensional horizontal plane and was due to horizontal isotropic turbulence. The study of horizontal diffusion using this approach has permitted prediction, with some success, of the spread of introduced substance (Joseph andSendner, 1958, 1962;Ozmidov, 1958;0kubo, 1962a). The importance of vertical diffusion, however, when combined with vertical shear in a mean flow, should not be underestimated even though the diffusing material is prac- tically confined within a very thin layer. As a matter of fact, another approach based on the interaction of a shearing cur- rent with transverse mixing does give rise to horizontal dif- fusion at a scale comparable to that of the purely horizontal spread due to horizontal eddies (Bowles et al., 1958; Bowden, 1965; Okubo, 1966; Pritchardera/., 1966). Presumably, both approaches are partially correct; each supplements the other. We shall discuss the two approaches separately. RADIALLY SYMMETRICAL SOLUTIONS OF HORIZONTAL DIFFUSION DUE TO HORIZONTAL TURBULENCE The following discussion considers primarily the two- dimensional horizontal diffusion of a radioactive substance introduced instantaneously at a point in the sea. The motion of a patch of diffusing radioactive material is a sort of irregu- lar spreading superimposed on an overall wandering of its center of mass. The wandering motion is attributed to the combined motion of large-scale currents (see previous sec- tion). On the other hand, the spreading of the patch is con- trolled chiefly by eddies whose size is comparable to or smaller than that of the patch. We are interested mainly in discussing the distribution of radioactive material about the moving center of mass. At any time after release, the shape of the isolines of any concentration will be very irregular (Figure 16); the patch of radioactivity will usually be elongated in one direction or another. In the discussion that follows, we shall visualize an infinite number of releases under identical oceanographic conditions, using for each the same amount of radioactive FIGURE 16 Patterns of dye patch on a horizontal plane. (Re- printed with permission from Joseph et al., 1964.) material. The centers of mass of the different patches will have different histories owing to the nonstationary and non- homogeneous character of the large eddies. However, as far as the relative distribution of substance with respect to the center of mass is concerned, certain statistical properties of individual patches may be almost equivalent from one patch to another since the smaller eddies responsible for the rela- tive diffusion are supposed to be stationary and homogene- ous (and probably even isotropic) in a horizontal plane. Thus, if we take an infinite number of distributions, each observed after the same time interval following release, and if we superpose them in such a way that the centers of mass coin- cide with each other, and if we average all of the superposed distributions, we would then expect a radially symmetrical distribution of substance about the center of mass, which at the same time would be the point of maximum concentra- tion, provided that the mean flow pattern is isotropic. In other words, the mean concentration is a function only of the diffusion time, /, and the distance, r, from the center of mass. The very irregular distribution of concentration in the individual release can be regarded, so far as the rate of dis- persion is concerned, as a particular realization from the ensemble from which the averages are formed; thus, the area

108 Radioactivity in the Marine Environment enclosed by a line of constant concentration at a time, t, after release, would be nearly the same for all the identical releases. We shall now discuss a possible form of the radially sym- metrical distribution. Assume that, with the passage of time, the pattern of concentration relative to the maximum con- centration at the center of mass remains relatively unchanged as the characteristic length of dispersion grows and the peak concentration decreases. We may express this formally as S(t,r) = - sb(t) (6) where S0 (t,o) represents the peak concentration at the center of mass of a radioactive patch, b(t) is the characteris- tic length of dispersion, F is a decreasing function of the argument r/b, and the factor e~*' represents the decay of radioactivity. Since the total amount of radioactive material released over a period of time is conserved if radioactive decay is taken into account, we have oo / 5(r,r) e*1 2.nrdr = M/D, (7) where M is the total amount of material released, say, so many curies, and D is the depth of water within which the radioactivity is assumed to be distributed uniformly. The substitution of Eq. (6) into Eq. (7) yields M1D S0(t,o) = where $ is a form-constant, its value dependent upon the pattern of concentration. Hence, we write \b(t) (8) Other physical concepts must be introduced to determine the forms of F and b. One possibility, a Markov-process hypothesis, leads to an exponential pattern for F. Thus far, proposed solutions that can properly describe oceanic horizontal diffusion are mostly of an exponential type. They are, apart from the decay factor: s, = 1 M1D 1 --(ra//»3,3) p-(rlpt) (Joseph and (q. Sendner, 1958) w (Okubo and (101 Pritchard, 1960) l ' (Ozmidov, 1958) (H) (Obukhov, 1959) (12) (Okubo, 196 2a) (13) 4ff In particular, a Fickian solution is obtained when b = 4kt, where k is a diffusion constant; that is, .} = ' e-(r2/4fc») S, = (14) As is well known, Fickian diffusion fails in describing hori- zontal diffusion in the sea (Stommel, 1949). The Schonfeld solution (1959) does not belong to an exponential type; it is a special case of the similarity solution, Eq. (8), when b = cor and -3/2 (15) Table 4 presents some theoretical results derived from proposed solutions. They predict that the maximum concen- tration decreases as either r2 or r3 after the effect of radio- active decay is eliminated. Dye-release experiments reveal that the exponent of t lies, in general, between -2 and -3 (Okubo, 1962a) and sometimes varies even in the course of diffusion (Pritchard etal., 1966). A similar situation is found in the spatial distribution of concentration; any one of the proposed solutions is able to fit, to some extent, the observed distribution. All of the proposed solutions, except Schonfeld's, show that the variance, i.e., the mean square distances from r = 0, increase with time as either r2 or t3. The Schonfeld solution is the type of Cauchy's distribution for which no moment of positive order is finite (Cramer, 1945). An ever-increasing power of dispersion is character- istic of the horizontal diffusion due to oceanic turbulence. For a Fickian diffusion, the variance is proportional to time so that a constant coefficient of diffusion may be defined.

Physical Processes of Water Movement and Mixing 109 TABLE 4 Some Theoretical Predictions Derived from Proposed Solutions Proposed Solution by" Peak Concentration, Spatial Distribution, In Sj(t,r) Horizontal Variance,* a2 Joseph and Sendner Okubo and Pritchard 2 Ozmidov - I ,2/3 yt 60y3t3 Obukhov -3 03,3 1 r3 ' r4'3 4 aV Okubo 3/4 ir^a3 a2f2 \J TT 1 r2 1n w31 Schonfeld Inw2 (w^^ + r )^/^ "Refer to Okubo (1962b) for further references and details regarding these solutions. 6Horizontal variance is defined as the mean squared value of the horizontal distance of substance particles from the center of mass. Mathemati- cally, it is expressed by oo oo = I) (x2 + y2)Sjdxdy = I r2Sj(r,t) 2*rdr. For oceanic diffusion, on the contrary, the variance increases faster than r1, so that an apparent coefficient of diffusion increases with time or with the scale of diffusion, /, e.g., the size of a diffusing patch of radioactivity. Roughly speak- ing, as the size of the patch increases over the course of time, its diffusion will be more and more subject to the large-scale eddies, which contain more energy than the small eddies, and consequently, the rate of dispersion will be ac- celerated. It can be shown that the r3 law of the variance is equivalent to the I4/3 law of an apparent coefficient of dif- fusion, where / represents the scale of diffusion, say, the standard deviation associated with the distribution. The 4/3 law of diffusion was first proposed by Richardson (1926) for atmospheric diffusion, and later by Stommel (1949), Inoue (1950), Ichiye and Olson (1961), and others, for oceanic diffusion. On the other hand, the t2 law of variance corresponds to the /i.0 law of an apparent coefficient of diffusion. It goes without saying that the radioactive decay does not affect the variance of the concentration distribu- tion in a patch. The proposed solutions can also be classified into cate- gories on the basis of a characteristic parameter involved in the solution. One group contains a "diffusion velocity" as a parameter [see solutions (9), (10), and (15)], and the others are characterized by the rate of turbulent-energy transfer (cm2/sec3). The basic concept involved in the latter group of solu- tions is that the eddies responsible for the horizontal spread of substance lie in the "inertial subrange" (Kolmogorov, 1941). These eddies receive their energy from the larger eddies and pass it to smaller ones. No direct energy is sup- plied to those eddies from external sources, and the energy dissipation due to viscosity is not significant. Their proper- ties thus depend only on the rate of energy transfer, which

•t o o X X 2 *^ -7 3 —l f*1 J / / '3 777 m 3• j^ 000 0 0 o H XXX X X - O VI Os *N 00 (N Tf p> O rs — * oo so r- ^H pi O 0 M X X aa oo v> « ^ *4 '5 o 777 J J ~ o o o o 0 3 XXX X X c O OO 00 1O 00 NO f; 09 ~H O t-- 1O NO O M on »~I ^ ^ 1~1 *o X 09 « X 8 ^-* fl c o 777 J J s rt o o o o o 2 XXX X X c O t- CTN — ( -. sO oo l/> C/5 — * O v> ^ IO O 1* fl 777 VI V o o o o O i X X X I X X — - -H *N ^ m * m n rs n It i i i 0 O O ln i U C 1 1 X X X I o X o ss § o IK! V> 0 3 u « >, 777 *n 1n £ CM .^ o o o o 0 « ai — 1 O c XXX X X =3 is S 00 (N O> O t- -H °i p- O U! O -H O (N »4 ' ~H 00 toO £ j) 777 r- 7; M o^ 000 o o •o 1 0 1 XXX X X 1 E 'S1 O - ri f — ^ i OH m ft) o *-* c (£ a o 0 •JJ 'o"JJ it *f> ii ^^ ^^ */5 sn 35 .^- 1 4} n •t •g'e C6r6 •E r O (D 13 ca Cd 32 a, 3 ?- oa. ,j 3 I *o a CO ll If ll kubo (19( •i |l II c • I* lr> i •o •o «« its 1I O TABLE Proposed Solution Diffusion (time 'O *-s "Refer to .— E 0 E u — ' I- t/5 110

Physical Processes of Water Movement and Mixing 111 10'6 - IO14 - - I0'z "E 0 M *y.*ke and Saruhashi (1958) • Fo1som and Vine (1957) > Chesapeake Bay Institute (unpub1ished 1960) * Chesapeake Bay Institute (unpublished 1962) v Munk, Ewing and Revelie (1949) ° Seligman(1956) o/ Gunnerson (unpub1ished 1956) x 0kubo era/. (1957) 102 10' I06 t(sec) I08 1O10 FIGURE 17 Relationship between the horizontal a1 and time of diffusion, /. (For details, see Okubo, 1962b.) must be equal to the rate of energy dissipation if the energy of the eddies remains stationary. Under natural conditions, however, there is often the possibility of energy being added directly to such eddies by local storms, tidal currents, or, on a still smaller scale, by waves (Stommel, 1949; Ozmidov, 1965).* These excited eddies could not then be strictly in the "inertial subrange," so results derived from that concept would not necessarily be applicable. Ozmidov (1965), never- theless, suggests the existence of the local inertial subranges separated by two scales of eddies where influx of external *Long-term current measurements at depths of 50 and 100 m south of Bermuda were made by Day and Webster (1965). Using the tech- niques of spectral analysis, they obtained kinetic energy density spectra for currents. The spectra show dominant spectral peaks cor- responding to the local inertial period on the 100-m depth spectrum and nearly to the local inertial period on the 50-m depth spectrum. Both spectra also show a peak at zero frequency or very large-scale eddies, and a broad low peak centered on the semidiurnal tidal period. energy takes place. This, in turn, suggests that solutions of the Ozmidov, Obukhov, and Okubo types may be used lo- cally with a different value of the rate of turbulent energy transfer. As the scale of diffusion increases, the expected value of this parameter decreases, since the local supplies of energy tend to be transferred from the larger eddies to the smaller eddies (for some exceptional cases see Webster, 1965). Table 5 suggests, as a matter of fact, that the esti- mated value of the rate of energy-transfer parameter de- creases as the scale of diffusion increases. As a consequence, the results derived from these solutions would approach, to some extent, those parameterized by a "diffusion velocity." The "diffusion velocity" model, on the other hand, is based on an intuitive concept that the rate of dispersion depends only on a "characteristic" velocity. Since the oce- anic diffusion processes are a result of oceanic turbulence, a close connection between a "diffusion velocity" and the intensity of turbulence, i.e., the root-mean-square value of the fluctuation in velocity of the ambient water, must exist. The estimated value of the diffusion velocity is of the order of 1 cm/sec. Joseph and Sendner (1962), using a few avail- able observations, presented a "diffusion-velocity spectrum" that indicates a weak dependence of the diffusion velocity on the scale of diffusion. Constancy of each characteristic parameter would be desirable for the purpose of practical application of the pro- posed solutions to the horizontal diffusion of radioactivity from a source; actually, however, they vary with the inten- sity and structure of turbulence in the sea under considera- tion. A review paper by Bowden (1964) provides a general idea of oceanic turbulence. In Figure 17 we plot the observed variance of the hori- zontal distribution from an instantaneous small source against the time since release. A linear fit to all points gives a2 = 0.006 Xf2-5 (a: cm; t: sec). (16) An apparent coefficient of horizontal diffusion may be de- fined by AL = a2/4r. (17) Eliminating t from Eqs. (16) and (17), we obtain an empiri- cal relationship between the apparent coefficient of diffu- sion, Ka, and the scale of diffusion, /, which is arbitrarily defined as three times the standard deviation of the horizon- tal distribution o. Ka = 0.0087 X/1.2 (Ka. cm2/sec; /: cm). (18) Representative values of a2 and Ka for various times and scales of diffusion are tabulated in Table 6.

112 Radioactivity in the Marine Environment TABLE 6 Representative Values of the Horizontal Variance, a2, and an Apparent Coefficient of Diffusion, K Apparent Coefficient Diffusion Time, Horizontal Variance, Standard Deviation, Scale of Diffusion, of Diffusion, t a2 (cm2) a / = 3a (cm) Ka (cm2/sec) 1 hr 4.7 X106 22m 6.6 X103 3.3X102 5hr 2.6 X108 160m 4.8X104 3.7 X103 10 hr 1.5 X109 380m 1.1X10s 1.1X104 1 day 1.3X1010 1.2km 3.6 X 10s 3.9 X104 10 days 4.2X1012 20km 6.0 X106 1.2X106 30 days 6.5 X1013 80km 2.4 X107 6.0 X106 50 days 2.3 X1014 150km 4.5 X107 1.4X107 100 days 1.3X1015 360km 1.1X108 3.9X107 365 days 3.3 X1016 1,800km 5.4X108 2.7 X108 FIGURE 18 Dye patch 1 hr, 27 min after release, August 15, 1962. Wind direction is indicated by smoke bomb on sea surface, far right. Arrow points north. SHEAR-DIFFUSION SOLUTIONS Many aerial photographs of dye patches from an instantane- ous source reveal that they are more or less elongated. Fig- ure 18 is a photograph of one of these elongated dye patches. The dye, introduced as a vertical line source, began to elon- gate after about an hour and a half roughly in the direction of the local wind. The research vessel is approximately 30 m long. The leading portion ("head") of the dye patch con- tained a higher dye concentration than the trailing portion ("tail"). Observations revealed that the head is at or near the surface while the tail is at a lower level, probably several meters down. From the leading edge toward the tail, the dye was located at successively deeper levels. It is evident that the apparent elongation of the dye patch is a result of the vertical shear in the horizontal mean flow. A remarkable feature of the elongation is the clockwise curvature (when looking from the head toward the tail) of the tail. In almost all observations of elongation, the curva- ture, when present, was clockwise in the northern hemi- sphere; a few observations revealed anticlockwise curvature of dye patches in the southern hemisphere (Katz et al., 1965; Ichiye, 1967). This suggests that the curved tail may be due to the effect of the vertically differential advection by the wind-driven Ekman current, which is represented as a spiral on a horizontal projection. Katz et al. (1965) de- scribed schematically the development of the curvature by the Ekman flow (Figure 19). The elongation of a substance patch due to the differen- tial velocity in the mean flow gives rise to an effective dif- fusion when combined with transverse mixing due to small- scale random motions. Bowles et al. (1958), noticing the importance of this process in horizontal mixing, called it the "shear effect,"* by which they meant the distortion of a vertical column of substance due to the variation of mean *This effect has been recognized by fluid dynamicists since 'he be- ginning of this century. An analytical study of the shear effect on dispersion was first made by Taylor (1953, 1954) for the dispersion of solution through a tube and pipe, and also by Corrsin (1953) for an unbounded shear flow.

Physical Processes of Water Movement and Mixing 113 DYE PATCH (T2) WIND DYE COLUMN (I, SHADOW OF PATCH FIGURE 19 An idealized model showing the way a classical Ekman-type drift current in the northern hemisphere would distort a column of dye that initially extended vertically downward from the surface, d is the depth to which dye can be seen. D is the depth of penetration of the wind-induced current. 20 a > ou K Ca11 No 1 Ce11 No 1 2 • C B c E Oi1 No 1 2 3 B C E * I/ /* i/ 1 /4: ,.0 - BC.AD.2UT (b) 0 r f2T FIGURE 20 Longitudinal dispersion of a substance by the "shear effect." (a) Initial Condition; (b) t = 0; (c) t = T; (d) t = 2T. velocity with depth combined with vertical mixing. How- ever, any gradient of mean velocity combined with turbu- lent mixing leads to an effective diffusion. Thus, the shear effect (in a broad sense) may be associated with tidal cur- rents, inertial currents, density currents, wind-driven cur- rents, and so on. A very simple model provides a clue to understanding the shear effect (Figure 20). Consider a shallow basin of constant depth H. The mean horizontal velocity is assumed to vary linearly with depth only; its value is 2U at the sur- face and zero at the bottom. The shear effect is simulated in such a way that for an interval of time, T, shear alone acts to distort a patch of substance; then, vertical mixing occurs and instantaneously produces a uniform concentration throughout the depth,//. The process is repeated at another interval, T, dispersing the substance in the direction off/. Thus, after each interval T, a new cell of the length 2UT is added to the substance patch. It can be shown (Okubo and Carter, 1966) that after a time, nT = t, the distribution of substance among the cells is represented by a binomial distribution with the variance n (UT)2 = IP.T t. Since T is a measure of the time required for a given bounded system to attain substantial vertical homogeneity of material, 7* must be of the order ofH2/irKz, where Kz is the coefficient of vertical eddy diffusion. Hence, the downstream variance is of the order of U2ff2t/n2Kz; a more elegant and exact derivation gives t/2//2 t/3QKz (Saffman, 1962). This simple model implies that horizontal diffusion can occur even without horizontal components of random move- ments of water. Furthermore, the value of the variance due to the shear-diffusion may well account for the scale of dif- fusion observed in shallow waters (Bowden, 1965). For example, if we take U= 10 cm/sec, H= 3 m, andKz = 10 cm2/sec, then after t = 104 sec, the variance due to the shear diffusion amounts to 3 X108 cm2, or the size of patch is a few hundred meters. The shear effect, however, appears in a different manner when the region is effectively unbounded, because the sub- stance is allowed to diffuse indefinitely in the direction of shear, i.e., perpendicular to the mean velocity. The effect of shear on dispersion will be far more marked in an un- bounded region than in a bounded one. For a uniform shear field, in fact, the longitudinal variance increases as t3 in an unbounded region (Corrsin, 1953), whereas the variance is a linear function of time for the bounded case. For this rea- son, we shall first present a shear-diffusion model in an in- finite sea and later consider the possible effect of boundaries. In the radially symmetrical model, no allowance is made explicitly for factors such as shear in the mean flow. The shear-diffusion model, on the other hand, focuses attention on the actual pattern of flow that can contribute, together with the random motions of small-scale eddies, to the mix- ing. For simplicity, assume the mean velocity field to be sheared both laterally, J2 and vertically, £2Z. They are con- sidered to be steady and homogeneous, that is, U= U0(t) - Slyy-n,z, V = W = 0, where U0(t) is the time-dependent mean velocity in a plane y = z = 0. Since the time-dependent homogeneous flow has nothing to do with the spread of radioactive material with

114 Radioactivity in the Marine Environment respect to the center of mass of the patch, we simply take a coordinate system whose origin moves with the center of mass of the patch with its x-axis directed with the mean flow, the -y-axis lateral, and the z-axis vertical. We thus elimi- nate the U0(t) term completely from our discussion. We further assume that the small-scale eddies responsible for the internal mixing can be described by eddy diffusivi- tiesAx,A and^2 in thex,^, andz directions, respectively. These are taken as constant in order to make the problem tractable. The basic equation for the shear diffusion is then ex- pressed by 35 - + (-n v - 35 - 3x the shear effect is hardly felt. A critical time, tc, may be de- fined by 4>3i . For the main period of shear diffusion, i.e., t > &3l, the following features are derived from equation (20): maximum concentration, ,-2.5 x-vanance, ^-variance, a2 = 2A t 325 325 325 = Ax — + Ay— + Az — - X5. (19) 3x2 3y2 3z2 z-variance, a2 = 2Az t The solution for an instantaneous point source at x =y = z = Ois mean horizontal variance, -2 = - - = T j U — UUV L /\.. x y ' degree of elongation on a horizontal plane, 8;r3/2 exp- (20) where 5; represents the concentration from a unit amount release, say, a 1-Ci source, with no decay, and 4>2 is defined by (1/12) [n2 (Ay/Ax) + n2 (AJAX)\. It is interpreted that 4>ji represents a time at which the shears come into effect on mixing of substance. Equation (20), having a quadratic form in x,y, and z, states that the contours of the concentration are a set of ellipsoids with common principal axes, the orientation of which varies with time. Thus, the patch of radioactive ma- terial is elongated in general. The degree of elongation de- pends, apart from r, on the shears and eddy diffusivities. A long time after release, a very much elongated patch will line up in the direction of mean flow, and, at the same time, the combined effect of the shears and of the diffusion due to random eddies accelerates, to a great extent, the rate of dispersion of radioactive material around the moving center of mass. For an initial period of diffusion, however, t-i 02 . Q2z 3 ">, + 12 "^ A apparent coefficient of horizontal diffusion, Ke = - = Ay 2t 12 "^T Equation (20) describes three-dimensional diffusion under shears in an infinite ocean. For a release in the surface layer or near the bottom of the sea, we must take into con- sideration the (reflective) boundary effect at least at the sea surface ("naviface") or at the bottom; a lateral boundary such as a coastline may be treated in a similar way. Without the shears, or for the radially symmetrical model, it would be easy to treat the boundary effect simply by adding the image of the fundamental solution for infinite space with respect to the boundary (Carslaw and Jaeger, 1959). With shear we cannot use the image method in such a simple way, as might be expected. However, the essential features of the shear diffusion

Physical Processes of Water Movement and Mixing 115 would remain much the same for infinite and quasi-infinite seas, except for the fact that the distribution in the vicinity of the boundary becomes asymmetrical in that the position of the maximum concentration shifts toward the down- stream direction. Saffman (1962) shows, as a matter of fact, that the longitudinal variance for the semibounded case dif- fers only by a certain numerical factor from that for the infinite case. Obviously, the presence of the boundary does not affect the lateral and vertical variances. These results also indicate that the time behavior of the peak concentra- tion would be unchanged. In shallow waters the presence of both the sea surface and the bottom must be considered after an appreciable amount of the substance has diffused from the surface to the bottom. Then the shear diffusion due to vertical shear becomes decelerated and will be overwhelmed by the shear diffusion due to lateral shear. In other words, the depth- mean concentration can be discussed by a two-dimensional shear-diffusion model with the effective value of the longi- tudinal coefficient due to vertical shear (Bowden, 1965) added.linearly to the eddy diffusivity,.4x. The solution for the two-dimensional diffusion in a hori- zontal shear can be easily obtained by putting S2Z = 0 in Equation (20) and taking an average over the depth,/). We then have ~ V3 , = -S^- t-* Me-\t 4nD(A'xA J1/2 t]/\ exp - 4,4; (21) where 3>2 = 12 £ly \]Ay/Ax, D denotes the mixing depth over which the substance is distributed uniformly, andv4' is the sum of Ar and the effective longitudinal coef- l ficient due to vertical shear. $j is interpreted as a time at which the horizontal shear begins to come into effect on the mixing of substance. The behavior of the characteristics of two-dimensional shear diffusion may be summarized as follows for f > ^j1: «-2 Sl a2 = \Ay r1 y = 2 Ay t y 1 Essential features of the shear diffusion are the same for the three-dimensional and two-dimensional cases. The faster rate of decrease of the peak concentration in the three- dimensional case is simply a consequence of the fact that the substance has one more dimension to diffuse. Carter and Okubo (1965) analyzed dye-release experi- ments in the Cape Kennedy area purely on the basis of shear-diffusion models. Offshore releases, being regarded as three-dimensional cases, exhibited the two time regimes, t~l.s and t~2.5, in the decrease of the maximum concentra- tion (Figure 21). On the other hand, near-shore and inshore releases in shallow waters showed the two time regimes, t~ia and t~2.°, in the decrease of the peak concentration. For both the deep- and shallow-water cases, the horizontal variance increased in direct proportion to the second power of time. Representative values for the shears and eddy dif- fusivities in the offshore region of the Cape Kennedy area are estimated as follows: Winter Summer n. 4X103cm2/sec 19cm2/sec 1.8 XIO-3 sec-1 <1(H sec-1 4hr 4X103cm2/sec 1.3 cm2/sec 6.6 X 10-3 sec-1 <10-4sec-1 8hr As may be seen, there is an interesting resemblance be- tween this simple shear-diffusion model and a "diffusion velocity" type of solution of the radially symmetrical model. Both models give the same dispersion rate: the horizontal variance increases as the second power of the time. As a matter of fact, a combined parameter, say, \/Sl Ay, which appears in the expression for a2 in the shear-diffusion model, has the dimensions of velocity. Using the values of shear and eddy diffusivities shown above, we obtain a value for the combined parameter on the order of 1 cm/sec, which is comparable to the value of a diffusion velocity estimated in the radially symmetrical model. This implies that the shear-diffusion model describes more explicitly the physical processes of horizontal diffusion from a source than the radially symmetrical model does. CONTINUOUS RELEASE FROM A FIXED POINT As mentioned earlier, the solution for an instantaneous source is not necessarily fundamental to the construction of the solution for a continuous source. However, there are no

116 Radioactivity in the Marine Environment FIGURE 21 Variation of peak concentration with time for dye- release experiments in the sea off Cape Kennedy. (See Carter and <)k Mb,,, 1965.) o t z D Z 2 - 10-' -1 z 5~ APRIL "0 RELEA5E# 3 i O RELEASE *4 AUGUST A RELEASE «5 1 D RELEASE #6 D( 51020 501002005001000 T1ME (H0URS) appropriate differential equations to be used as a basis for oceanic diffusion from a continuous source. It still seems appropriate, however, to consider plume-dispersion models, such as that of Frenkiel (1953) with an eye toward practical applications. Plume-dispersion models in widespread use employ in- stantaneous patches as elementary components. The ideal plume model is assembled by superposition of an infinity of overlapping instantaneous patches, each released from a fixed origin and each translated by the mean velocity, U. Such a superposed-patch model is illustrated in Figure 22a. Thus, the concentration of radioactivity from a continuous source may be formulated as follows: C(t,i t = f -Ut',y,z)e-^'dt', (22) where C(t,x,y,z) denotes the concentration of radioactivity at a point (x,y,z) and at a time t, elapsed since the start of releases; q(t) is the rate of release at the source in curies per second; and S7 represents the concentration distribution for an instantaneous release of a unit amount without decay. Any one of the solutions for an instantaneous release may be used for 57. Only a few limited cases, however, per- mit one to carry out the integral in Eq. (22) analytically. For mathematical convenience, therefore, diffusion in the direction of the mean flow is neglected, leading to the "spreading-disk" model for plumes, as illustrated in Figure 22b. Thus, the formula for Cin the disk model becomes C(t,x,y,z) oo '-0 f SI(t',x'-Ut',y,z)dx'e-^'B(x-Ut')dt' 'x~x'y'z andOforx>l/r. ±Ut (23)

Physical Processes of Water Movement and Mixing 117 To illustrate, let us take the instantaneous solution (Eq. 10). The depth mean concentration from a continuous source is given by C(t,x,y) exp- and 0 for x > Ut. U (24) That is, the centerline concentration in the plume from a constant rate of release without decay decreases inversely with the distance from the source. Similarly, the instantaneous solution (Eq. 12) results in the following expression for the depth-mean concentration: C(t,x,y) ""§ exp - exp - — FIGURE 22 Schematic plan views of plumes: (a) ideal (theoretical) plume; (b) spreading-disk plume; (c) fluc- tuating single plume. (See Gifford, 1959.) for x - Ut mean concentration at a fixed point may be expressed as follows: and0forx>£/r. (25) 00 iC(t,x,y,z)I = J C(t,x,y-y0,z)g(x,y0)dy0, (26) Here, the plume concentration along the central line de- creases in proportion to x~3/2 when the rate of release is constant and the decay is not included. The three-dimensional shear-diffusion solution (Eq. 20), when applied to the centerline concentration of a constant release plume, also gives rise to an x~l law. Real plumes present a far more complicated appearance (Figure 22c) than does the plume of the theoretical model. The motion of the individual elementary patches consists of two parts: spreading within individual patches and meander- ing of the center of mass of the element. The meandering is caused by the motion of the large-scale eddies. However, if we focus our attention on a meandering plume at a given instant and position a coordinate system with respect to the meandering plume, i.e., the x-axis along the centerline of the plume, the concentration distribution in the plume can be represented by the ideal plume discussed above. On the other hand, the mean concentration at a fixed point taken over a certain period longer than the time scale of the meandering will be smaller than the concentration in the ideal plume. According to Gifford (1959), a long-term where g(x,y0) represents the frequency function associated with the meandering of the central line of a plume about the x-axis, i.e., the direction of the overall mean velocity, um. Thus far, very few experimental and theoretical results concerning the frequency function appear to have been re- ported. If it is assumed that the frequency function is Gaussian with the variance ag(x), Eq. (26) can be integrated, at least in principle, for appropriate solutions for the ideal plume, C. Thus, the depth-mean solution (24) for C com- bined with a Gaussian form of g gives (Gifford, 1959): iC(x,y)I = a2)!/2 exp - 2U, •exp-[t;] (27)

118 Radioactivity in the Marine Environment where the rate of release is assumed to be a constant value, q0. Csanady (1963) showed experimentally that the stan- dard deviation, ag, increases linearly with the distance from the source. This implies that the overall mean concentration along the x-axis, without radioactive decay, still decreases inversely with the distance, with an effective diffusion ve- locity larger than that of the ideal plume. Another important aspect of continuous releases must be mentioned. That is, from the standpoint of a safety estimate of radioactivity, not only the concentration in a steady-state portion of the plume but also the distribution of radioactiv- ity in the transient-state portion, e.g., the advancing front of the plume, must be considered. The "disk" model is too crude to be used for this purpose, because the longitudinal diffusion of individual elementary patches primarily deter- mines the concentration distribution in the frontal part of the plume. We must return to the general solution (23), sub- stitute an appropriate instantaneous solution into 5}, and perform the integration. Let us consider a tractable case, in which the duration time of release is very short in comparison with the half-life of the radioactive isotope in question. Then, using solution (10) for Sj, we obtain the concentration from a constant rate of supply as follows: C(f,x,y) erfc (28) where 2 C 2 erfc TI = e~°. da, and xr = Ut. •JW J i In particular, the centerline concentration becomes C(t,x,o) « forx^0. erfcl- — (29) At the point x = xr, the concentration is half what it would be if the source had been emitting for an infinite time. Be- yond this point, the decrease in concentration is very sharp, depending upon the ratio of the values of the mean velocity and of a diffusion velocity. Figure 23 illustrates schematically how the centerline concentration varies with the distance for a transient plume from a continuous source. 1og C(t,i,o) FIGURE 23 Schematic variation of the centerline concentration with distance, for a transient plume from a continuous source. Equation (29) appears to satisfy some of the observed features of the oscillating plume in a tidal estuary (see Carter, 1965). FINITE SOURCES Thus far, we have regarded the size of the source as infini- tesimal. This means that the discussed solutions cannot be applied to a certain initial period of patch diffusion or in the vicinity of a continuous source, since the source is actu- ally finite. A measure of the critical time or distance beyond which a point-source solution is practical is discussed below. First, consider an instantaneous release. Let a2 be the variance of the initial distribution from a finite-sized source. Then, the critical time, /y, is defined as the time at which a2 ((y) = a2, where a2 (/y) denotes the variance from an in- stantaneous point-source. For practical purposes, the finite-source problem may be treated by the method of superposition of infinitesimal sources, even though this method is not correct in principle. Thus, the depth-mean concentration from a uniform source of rectangular shape, extending from -a/2 to a/2 in the x direction and from -b/2 to b/2 in thejy direction, can be expressed as follows: Sf(t,x,y) a/2 6/2 = -Sri f dx0 f dy0s'(t'x-*0'y~ abD 1 J J -a/2 -6/2 <>-*1, (30) where m denotes the amount of radioactivity released per unit area. Similarly, continuous releases of radioactivity from a finite source can be treated by superposition. Thus, beyond the distance Xf = Utj. from the source, we may, for practical

Physical Processes of Water Movement and Mixing 119 purposes, disregard the size of the source; there the distribu- tion of radioactivity would be nearly identical to that at a point source with the same total intensity. OCEANOGRAPHIC IMPLICATIONS OF THE DISTRIBUTION OF NATURAL TRACERS AND FALLOUT ISOTOPES The development of radioactive tracing and dating tech- niques in the last decade has provided oceanographers with a new tool for studying large-scale (oceanic) physical pro- cesses in the sea, such as diffusion and advection. We may hope that as tracer measurement techniques improve, our understanding of the worldwide distributions of these radio- active tracers will also improve, thus permitting us to focus our attention on smaller scale processes. As our understand- ing of the processes of advection and diffusion at all scales improves, so too will our ability to predict the capacity of our environment to receive radioactive wastes, from fallout and other sources. Accordingly, this section reviews the radiochemistry literature that applies to the oceans. Since most of the papers reviewed analyze the data by means of "box models," it seems appropriate to start with a general description and discussion of these models. FLUID SINK- -* CJ E) -,Cj RESERV0IR j T 1NTERFACE I I r I RESERVOIR i 0,., C, FLUID S0URCE FIGURE 24 Schematic presentation of the transfer processes between two reservoirs. is assumed that Cj>Ct and that continuity of mass is main- tained by a fluid source in reservoir / and a fluid sink in reservoir/ at unspecified points in these reservoirs. At steady state, we have at the interface QH " c, + EH " q -EH" q = o. (31) Equation (31) may be rewritten as follows: QH EH .Nt + -J..Nf -^-l. M=0, (32) ,t where — = C,. Box Models Radiochemists are generally credited with developing the box model concept, although similar models were used in the early stages of the study of physical oceanography. Radiochemistry data is analyzed by this means probably because such data are sparse, and an oversimplified picture of the ocean is required in order to draw any conclusions at all. In this approach, the ocean is divided into a number of "boxes," or reservoirs, each containing water that is assumed to be well mixed. The entire system is generally assumed to be in a steady state, and the exchange of fluid-attached properties, i.e., salt, heat, stable carbon, 14C, etc., is as- sumed to take place in accordance with first-order kinetics- that is, the transfer of matter follows an exponential ex- change law (the flux of the property per unit area per unit time is proportional to the concentration of the property) as long as the internal mixing rate in each reservoir is large in comparison to the transfer rate out of the reservoir. The transfer processes are unspecified, although one physical interpretation may be arrived at as shown in Figure 24. Consider the interface between two liquid reservoirs such as those shown in Figure 24. Here, there is an advective flux of property Qt-j • Ct from reservoir i to reservoir /, and a net diffusive flux £•, . • Q - Ej-t • Cj, in the opposite direction. It Finally, from Eq. (32), we obtain (33) where ^ —— = k.-. = (advection) 'i ' T0d '-i (diffusion) TM 1 = k]-, = — (diffusion) (34a) (34b) (34c) and where rt-j is the residence time, or "average" life, of a molecule of the species being considered in the reservoir /' relative to the reservoir/. T^ is identical with the T defined

120 Radioactivity in the Marine Environment in Craig (1957) as the quotient of the steady state contents of a reservoir and the flux. An expression that is completely equivalent for the same exchange at the interface and for the form that is usually used in box models is v/ = 0. (35) Thus, one possible interpretation of residence times arrived at by use of equations similar to Eq. (35) is that the transfer coefficient, &•-,., is some measure of the diffusion and &,.-.• is some measure of the combined effects of diffusion and ad- vection, since fc,.-;. corresponds to fc«f. + WW in Eq. (33). Another important conclusion concerning box models of the chain* type may be drawn from Eqs. (32) through (35). A chain model does not permit a net flux of water mole- cules across the interface except for the evaporation-precipi- tation difference at the air-sea interface. Such a model is shown in Figure 25. The water balance requires that ED-M = EM-D at steady state, and from Eqs. (34b) and (34c) we have, (36) or TD-M JM-D (37) These relationships indicate that the residence times deter- mined by this model will depend quite critically upon the mixed-layer depth that is selected. Models of this type were used by Craig (1957, 1963), Broecker (1966), and Plesset and Dugas( 1967). Still another consideration is the strong interdependence between the model selected and the relationship between residence time and radiocarbon age. Attention has already been called to this by Craig (1963). In Figure 26, the resi- dence time of the ocean reservoir is very nearly infinity, since water can only be exchanged between the atmosphere and the oceans by evaporation and precipitation. That is, if the ocean were completely mixed by some means, the re- sulting "age" would refer only to the residence time of the radiocarbon molecules in the ocean relative to those in the *In a chain model, the reservoirs are arranged like beads on a string. If the deep ocean reservoir depicted in Figure 25 is ventilated by exposure to the atmosphere, the model would become a "cyclic" model with respect to 14C, but would remain a "chain" model with respect to water molecules. ATMOSPHERE / kM-ANM . kA-M'NA t 1 . ' MIXED * , | LAYER NM i 1 kD-MND kM-D'NM DEEP OCEAN FIGURE 25 A box model of the ocean- atmosphere system of the chain type. ko-o ATMOSPHERE NQ SOURCE ko-a N, OCEAN No FIGURE 26 A simple box model of the ocean-atmosphere system. atmosphere, and not to the residence times of the water molecules. In the situation represented in Figure 25, the radiocarbon and water molecules in the deep ocean can be exchanged only with molecules in the mixed layer; there- fore, if such an ocean could somehow be created, the resi- dence times of the deep ocean water and of the radiocarbon molecules would be identical. If one now ventilates a por- tion of the deep water by exposure to the atmosphere, such as occurs at high latitudes, the radiocarbon age of the deep water will be reduced, since the radiocarbon molecules in the deep sea can now be exchanged with those of both the mixed water just above and the atmosphere. The residence time of the water molecules is, however, unchanged. It is

Physical Processes of Water Movement and Mixing 121 apparent from the foregoing discussion that the residence times of interest to the oceanographer are the residence times of the various water reservoirs relative to each other, such as a deep layer relative to a mixed layer or an interme- diate layer relative to an overlying surface layer and an underlying deep layer. Any model that does not provide accurate estimates of the residence times of the water mole- cules in the various subdivisions of the real ocean is of lim- ited value in interpreting circulation patterns and mixing processes. At least three box models and one analytical model based on radioactive isotope data seem to meet the fore- going criteria. They are, in chronological order, the model of Broecker et al. (1961), the model of Bolin and Stommel (1961) for the Common Water* and Atlantic Intermediate Water, Broecker's (1966) transient-state model for predict- ing 90Sr and 137Cr vertical distributions resulting from bomb fallout and his steady-state model for the vertical dis- tribution of 14C, and Munk's (1966) analytical model for the deep Pacific water. Both the Bolin and Stommel model and the Munk model utilize, and are therefore consistent with, temperature and salinity distributions. These models are presented in Table 7. For comparison, even though they do not utilize radioactive isotope data, Montgomery's (1959) results for the residence times of subtropical surface water, based on his salinity model, are included. Table 7 summarizes what seem to us to be the important inferences to be drawn from the various models. It is quite clear that the average residence time of a water molecule in the deep Pacific and Indian oceans is about 1,000-1,300 years. Surface water in all oceans is 10 years old on the average, and Atlantic Antarctic Intermediate Water is 100- 400 years old. As used in this paragraph, "old" is synono- mous with residence time relative to all routes of removal. From continuity considerations, it is easy to deduce esti- mates of vertical velocities at the interface between the deep water and the water above it (interface depth approxi- mately 1,000 m). These vertical velocity estimates should be regarded as oceanic averages. Their order of magnitude is 0.3-1.4 X 10~5 cm/sec. It is not possible to separate in an unambiguous manner the effects of deep horizontal advec- tion and vertical mixing. The range of horizontal velocities for the northward velocity of the deep Pacific waters were arrived at by ignoring vertical diffusion for the lower limit and including its effect for the upper limit. Broecker's model (1966) is not consistent with what we believe to be the important processes in the formation of the thermo- cline, as he points out. It does, however, permit a compari- son between mixing rates inferred from 14C data, on one hand, and 90Sr and 137Cs data, on the other. *This is the deep water of the Indian and Pacific oceans, the most voluminous water mass of the world. It was named by Montgomery (1958). Comments about Some Conflicting Oceanographic Implications from Observations of the Vertical Distribution of 9oSr and 137Cs A number of investigators, notably Miyake et al. (1962), Bowen and Sugihara (1958, 1960, 1965), and Rocco and Broecker (1963), have measured 90Sr and 137Cs concentra- tions at the surface and at various depths in the ocean and have interpreted the concentration distributions they ob- served. Some of these oceanographic interpretations con- flict with each other, and some apparently conflict with the descriptions of physical processes in the oceans presented in earlier parts of this chapter. Miyake et al. described measurements of 90Sr and 137Cs made in the western North Pacific Ocean in 1958, 1959, and 1960. They found significant amounts of radioactivity at depths as great as 5,000 m. They ascribed this deep pene- tration of radionuclides to vertical eddy diffusion from a source in the surface layers, and they computed a vertical diffusivity from their observed depth distribution for the depth interval 1,000 to 4,000 m. Their value of 200 cm2/sec for vertical diffusivity far exceeds the values for the deep waters of the Pacific obtained by Munk (1966) as well as the values that can be deduced from the analysis of Bolin and Stommel (1961). Munk obtains estimates of Kz, the vertical diffusivity, using distributions of temperature, salin- ity, and 14C, and shows that the value he computes of about 1.3 cm2/sec is consistent with the distributions of radium and dissolved oxygen. Munk also showed that the associated value of the vertical velocity (1.2 cm/day), which is inti- mately tied to the value of K2 in his model, is consistent with the probable rate of production of the Pacific Deep Water. As Munk points out, the values he obtains for the vertical diffusivity and for the vertical velocity are consis- tent with the results obtained by Stommel and his collabo- rators in their manifold attack on the abyssal circulation (Stommel, 1957; Robinson and Stommel, 1959; Stommel and Arons, 1960a and b; Bolin and Stommel, 1961), and by Wooster and Volkman (1960), and Knauss (1962). We have no reason to question the values for the concen- trations of 90Sr and 137Cs determined by Miyake etal.\ however, we find that we must reject their hypothesis re- garding the source of the deep penetration of these radio- nuclides. Miyake's measurements were made following several series of weapons tests in the Pacific, involving detonations that could have produced close-in contamina- tion to considerable depths. It is also significant that the very extensive but unpublished measurements of 137Cs made throughout the North Pacific by Folsom (personal communication) during 1965, 1966, and 1967 do not show significant amounts of this isotope below a depth of about 400 m, even though these measurements were made after the accumulated fallout had more than doubled over that

122 Radioactivity in the Marine Environment TABLE 7 Summary of the Residence Times, r, the Vertical Coefficients of Eddy Diffusivity, Kz, the Vertical Velocities, w, and the Horizontal Velocities, v, Inferred from the Various Models Model Water Mass Exchanges with Kz wX 10s v T (yr)a (cm2/sec) (cm/sec) (cm/sec) Broeker et al. (1961) Arctic Atlantic Deep Water 45 North Atlantic Surface Water Arctic 10 South Atlantic Surface Water North Atlantic Surface Water 10 North Atlantic Deep Water Arctic, Antarctic 600 Antarctic North Atlantic Deep Water, Pacific and Indian Deep Water 100 Pacific and Indian Surface Water Antarctic 25 Pacific and Indian Deep Water Antarctic 1,300 Bolin and Stommel (1961) Pacific and Indian Common Water North Atlantic Deep Water, Antarctic Bottom Water, Pacific and Indian Intermediate Water 1,200 0.6 Bolin and Stommel (1961) Atlantic Antarctic Intermediate Water Antarctic Surface Water, Atlantic Deep Water, Atlantic Surface Water 100-400 0.3-1.0 Broecker (1966) Caribbean (upper 750 m) Layer below Sr90 C 4.86 1.5 9.5° North Atlantic (upper 750 m) Layer below Cs137 < 1.66 4.5 28.5c South Pacific (upper 750 m) Layer below 1 16" 0.45 y Pacific-Indian Ocean main thermocline Layer below C14 ' 19 0.4 2.5 North Atlantic Layer below 5 1.5 9.5 Munk (1966) Pacific (all > 1 km) Vertical advection and diffusion with upper 1 km 1,000d 1.3 1.4 0-07-1.0 (north) Montgomery (1959) North Pacific Surface «100m) High-latitude Surface Water, Low-latitude 2 1.6' South Pacific «230 m) North Atlantic «375 m) Surface Water, and Deep Water High-latitude Surface Water, Low-latitude Surface Water, and Deep Water High-latitude Surface Water, Low-latitude Surface Water, and Deep Water 12 23 1.4' 1.9*

Physical Processes of Water Movement and Mixing 123 TABLE? (Continued) Kz, (cm2/sec) wXl05, (cm/sec) V, Model Water Mass Exchanges with r, (yr)a (cm/sec) South Atlantic «190m) High-latitude Surface Water, Low-latitude 9 i.y - - South Indian «170m) Average (<213m) Surface Water, and Deep Water High-latitude Surface Water, Low-latitude Surface Water, and Deep Water High-latitude Surface Water, Low-latutide Surface Water, and Deep Water 10 l.5e \Ae "Residence time relates to exchange by all routes permitted by the model. Residence time in each 150-m layer computed from d/R where d is the layer depth, 150m, and R is the inter-reservoir mixing rate [L/T]. cR, the inter-reservoir mixing rate. ^Computed from w (mass of Common Water/surface area of Pacific); M = 6X1023g; s= 1.37X 1018cm2. e Estimated from d2/T. which existed at the time at which Miyake et al. obtained their measurements. Of more concern are differences in the observed vertical distributions of 90Sr and 137Cs obtained by Broecker and his associates, on the one hand, and by Bowen and Sugihara, on the other. Broecker argues that his observations in the North Atlantic do not show 137Cs radioactivity exceeding 2 dpm/100 liters and 90Sr radioactivity exceeding 1 dpm/ 100 liters below a depth of about 500 m. Broecker's mea- surements in the equatorial Pacific are lower than these levels for 137Cs and 90Sr for all but a few samples below a depth of about 300 m. The latest published measurements by Broecker and his associates are for 1963. Published measurements of 90Sr radioactivity by Bowen and Sugihara were for the most part obtained in the Atlantic Ocean between 16°N and 16°S during the period 1957 through 1961. These measurements show significant 90Sr radioactivity at depths as great as 2,500 m and also show secondary peaks at intermediate depths. Measurements made by both groups are reasonably con- sistent for the near-surface layers. Both sets of measure- ments show a maximum of radioactivity at the surface and a fairly rapid decrease to a depth of about 500 m. Below this depth Broecker and his associates show 90Sr radioac- tivity, or 137Cs radioactivity converted to 90Sr equivalents, of less than 1 dpm/100 liters (with a few exceptions, dis- cussed below), while Bowen and Sugihara show 90Sr radio- activity at depths between 500 and 2,500 m ranging be- tween 2.8 and 4.5 dpm/100 liters. The vertical profile is irregular, showing intermediate secondary maxima. Bowen and Sugihara have argued that their observations are consistent with what is known about the large-scale cir- culation. They do not consider that the 90Sr radioactivity they find below about 500-m depth penetrates downward through the thermocline at middle and low latitudes. They argue instead that the source regions for deep and interme- diate water masses in the North Atlantic occur in regions of relatively high fallout. The sinking of water at these sources and the subsequent southward movement of the interme- diate and deep water masses along surfaces of constant po- tential density could bring radioactive materials to the inter- mediate and deep layers at middle and low latitudes. The general concept proposed by Bowen and Sugihara is certainly a valid one. Some North Atlantic Intermediate Water appears to be formed in a region centered at about 50°N, and the source region for North Atlantic Deep Water is centered at about 60°N. Based on land measurements, fallout reaches peak concentrations just south of 50°N, and is still about 55 percent of the maximum at 60°N. The speeds in the core of the intensified western deep boundary current, which carries the North Atlantic Deep Water south- ward, are thought to be sufficient to carry water to the equator from the source region in about two years. En- route, however, this flow feeds the deep water volume of the entire North Atlantic. Evidence from analysis of natural tracers indicates that the mean residence time for the Deep Water in the North Atlantic is at least 300 years, and for the entire North Atlantic Deep Water, including its penetra- tion through the South Atlantic, the residence time has been shown to be 600 to 800 years. Any tracer added to the sur-

124 Radioactivity in the Marine Environment face source waters for the North Atlantic Deep Water in the last decade should be considerably diluted at middle and low latitudes at this time, even though the minimum transit time to the equator would be great enough to permit some radionuclides to reach the equatorial Atlantic at depths of 2,000 to 3,000 m within 2 years after injection at the sur- face source. The velocities associated with the intermediate waters formed in the North Atlantic are not well known, and exist- ing evidence indicates that this water mass is not formed in very great amounts. Certainly, the North Atlantic Interme- diate Water is much less important as a supplier of interme- diate-depth water than the Antarctic Intermediate Water. However, fallout at the southernmost latitude of the source of Antarctic Intermediate Water is very small compared to fallout in the northern hemisphere. Thus, radionuclides injected into the source waters of the North Atlantic Inter- mediate Water within the last decade should be highly di- luted at intermediate depths in the middle and low latitudes of the Atlantic. The problem we face in explaining the relatively high 90Sr radioactivity observed by Bowen, therefore, is not that there are no mechanisms that would ultimately bring radio- nuclides originally injected into the surface layers as fallout to depths between 500 and 2,500 m at middle and low lati- tudes, but rather that the radioactivity observed appears to be much higher than would be expected from known resi- dence times for the intermediate and deep water. According to existing concepts, the older resident water simply rep- resents too large a diluting volume for the recently initiated source of radioactivity. A recent compilation of all 90Sr and 137Cs measurements made to date, now being prepared for publication by the New York Operations Office of the Atomic Energy Com- mission, indicates that observations of the deep penetration of these isotopes are not restricted to Bowen and Sugihara, but occur in the data of Broecker and his associates as well as of others. Even in their published data, Broecker et al. (1966) show one analysis of a sample collected at a depth of 4,330 m in the North Atlantic (34°49'N, 70°49'W) that has a 90Sr radioactivity of 4.3 ± 1.8 dpm/100 liters and a 137Cs radioactivity of 7.0 ± 1.2 dpm/100 liters. Thus, it appears that physical oceanographers must examine the evidence from fallout studies in greater detail than they have to date. It is quite possible that existing concepts must be modified to account for the relatively rapid deep penetration of these isotopes in the Atlantic. Using a technique quite different from that of Broecker and his associates, Folsom (personal communication) has made extensive measurements of 137Cs in the North Pacific. This technique involves the in situ extraction of the 137Cs onto KCFC resin, and relative large volumes of water can be processed rapidly. Most of Folsom's measurements were made during 1965, 1966, and 1967, and they constitute a larger number of 137Cs measurements than has been made by any other single source. These measurements agree with those reported by Broecker et al. (1966) for the equatorial Pacific in that Folsom's observations also show statistically significant radioactivity confined above 300 m. Folsom's measurements show one feature not revealed by the observations of other investigators. Folsom finds very large peaks of 137Cs radioactivity occurring in thin, subsurface lenses within the seasonal thermocline. In situ recording salinometers also show thin lenses of anomolous salinity maxima and minima in this same depth range. Fission explosions produce 137Cs and 90Sr at a relatively fixed ratio of between 1.6 and 1.8. These isotopes are thought to be transported together and to exist in seawater in completely dissolved form without being subjected to any significant biological or geochemical transport. Conse- quently, it is possible to convert, within reasonable limits, observations of one isotope to equivalent concentrations of the other. Folsom's rather extensive sampling of the surface waters of the North Pacific for 137Cs can therefore be com- pared to a collection of all available surface analyses of 90Sr in the Atlantic Ocean that have been compiled, but not yet published, by Vaughn Bowen (personal communication). This comparison shows that for the same latitudinal bands, the amounts of 90Sr and 137Cs radioactivity in the North Pacific are at least twice the corresponding amounts at the surface of the North Atlantic. This difference cannot be ex- plained as resulting from the greater amount of close-in fall- out in the Pacific. Of approximately 200 megatons of fission materials produced in weapons tests to date, some 167 mega- tons, or approximately 84 percent, was injected into the stratosphere and would therefore return to the earth's sur- face as worldwide fallout. We are forced to conclude that the fallout nuclides are mixed in the surface layers of the North Atlantic to a depth about twice that to which such nuclides are mixed in the North Pacific. This finding is con- sistent with our existing knowledge of the vertical density structure in the upper layers of the two oceans. The surface data supplied by Vaughan Bowen clearly show the surface mixing to be seasonal. We have averaged the surface 90Sr radioactivity in the North Atlantic by lati- tudinal bands and by 6-month periods for the years 1961 through 1966. The two 6-month periods chosen for averag- ing were December through May (which we here designate as winter) and June through November (which we here des- ignate as summer). Figure 27 shows the winter and summer averages for the three latitudinal bands of 30-40°N, 40- 50°N, and 50-60°N. To illustrate our point, individual curves have been drawn through the average of the winter points for the three latitudinal bands, and through the aver- age of the summer points. Both sets of curves reach a maxi- mum in 1963-1964. The winter 90Sr radioactivity observa- tions are, however, about 30 percent lower than those in the summer, indicating that mixing occurs to greater depths in the winter. Studies of residence times of natural tracers in the vari-

Physical Processes of Water Movement and Mixing 125 50 45 40 35 I 30 *n 8 25 20 15 \ ** •-Ck f 1961 1962 I963 1964 Year 1965 I966 FIGURE 27 Average of surface 90Sr activity in the North Atlantic by 6-month intervals. Summer and winter averages shown separately. ous intermediate and deep water masses may help resolve the problem of interpreting the Bowen and Sugihara observa- tions of the vertical distribution of 90Sr. E. Schuert, of the U.S. Naval Radiological Defense Laboratory (personal com- munication), has made careful comparisons of two sam- pling and analysis procedures for the determination of 137Cs in the ocean. Schuert took samples at three stations in the eastern North Pacific, two stations in January 1967 at 32°N, 130°W and 32°N, 123°W, and the third station in June 1967 at 34°N, 134°W. Two series of measurements were made at each station. In one series, 1,000 liters of water were pumped in situ through a device containing KCFC resin to extract the 137Cs. In the second series, water samples were collected using the large-volume water sam- pler designed by Bodman et al. (1961), which is also the sampler used by Bowen and Sugihara since mid-195 8. The KCFC resin used in the first series at each station was counted for 137Cs activity before use, and this reading was subtracted from the activity determined after passing the seawater through the resin. In the second series, the sea- water samples were treated chemically to concentrate and isolate the 137Cs. For each type of sampling, the three stations showed in- significant differences. Both techniques gave surface 137Cs activities at all three stations of 200 to 210 dpm/100 liters. The radioactivity decreased sharply with depth. At 340 m, the KCFC technique showed 137Cs activity of 0.8 ± 0.5 dpm/100 liter, and below 400 m, no statistically significant 137Cs activity was found on the KCFC resin. The water samples collected using the Bowen and Sugihara technique, with subsequent chemical treatment before analysis, showed that the 137Cs activity also reached essentially zero at about 400 m. However, a secondary maximum of 12 dpm/100 liters was observed at about 500 m, and another of about 5 dpm/100 liters at about 800 m. It has generally been assumed that both 90Sr and 137Cs exist in seawater in completely dissolved form, and that no particulate transport is involved in the distribution of these isotopes. Thus, any method that satisfactorily extracts dis- solved 90Sr and 137Cs should be suitable for the determina- tion of the distribution of these isotopes. Presumably, the KCFC resin removes only the dissolved 137Cs. Both the water and its contained suspended materials are treated chemically. One possible explanation for the differences in the vertical distributions observed by Schuert using the two methods of sampling and analysis is that cesium exists in seawater in two forms. Though the amount in true solution dominates, some small fraction may exist in particulate form. The KCFC method did not show any 137Cs in solu- tion below a depth of 400 m. The water sampling method, on the other hand, showed low but significant radioactivity at several depths below 500 m, which may have represented 137Cs associated with suspended particles that had reached these depths by gravitational sinking. One further piece of evidence may be cited. In a paper presented at the meeting of the American Chemical Society on October 3-7, 1966, D. E. Robertson and R. W. Perkins, of Battelle Memorial Institute, Pacific Northwest Labora- tory, described a series of 137Cs analyses made in the North Pacific. Their data represented the average of 10 vertical profiles taken along 39°N between 134° 15' and 134°59'W. This average profile is shown in Figure 28; the 137Cs activity is expressed in pCi/100 liters. Note that at 270 m the 137Cs activity decreased from a near-surface maximum to levels below the detection limit. This profile is relatively smooth compared to those observed by Folsom (personal communi- cation). The data is consistent with the measurements made using the KCFC method in that no detectable concentra- tions were found below approximately 300 m. We have in- tegrated this curve vertically and found that the accumu- lated 137Cs corresponds to a total fallout of 85 ± 18 mCi/ km2. This may be compared to a value of 115 mCi/km2 estimated for this latitude from land measurements. The difference (30 mCi/km2) may result from any of the follow- ing: (a) the fallout over this area of the Pacific may not be the same as the average over land for this latitude; (b) the counting uncertainty was quite high (this could account for a significant portion of the difference; note that the upper limit of the range of standard error would give an integrated value of 103 mCi/km2); (c) 137Cs may exist below the 270-m depth at concentrations just below the limit of de-

126 Radioactivity in the Marine Environment tection and through a sufficient depth range to contribute the 30 mCi/km2 difference to the depth integral; (d) 137Cs may exist both in the upper layers and below the 270-m level in the form not measured by the technique employed. The difference of 30 mCi/km2 is regarded as relatively small, and of opposite sign, compared to that reported by Bowen and Sugihara (1965). These investigators found that the depth-integrated profiles of 90Sr for the equatorial Atlantic showed amounts eight times higher than those ex- pected from fallout, determined from land measurements, in this latitudinal belt. In the next section, some recent measurements of the vertical distribution of bomb-produced 14C in the northeast Pacific Ocean are discussed. These measurements also sup- port the contention that in the Pacific, bomb-produced radionuclides that are primarily waterbound (i.e., in true solution) have not penetrated in measurable amounts below a depth of 300m. Estimates of Vertical Velocity and Vertical Diffusivity through the Thermocline Based on the Temporal Change in the Vertical Distribution of Carbon-14 Produced by Weapons Tests The use of the distributions of 14C and stable carbon in box models to estimate residence times of the various subdivi- sions of the oceans, as described earlier in this chapter, in- volved the use of measurements made prior to large weapons tests and subsequent correction to post-weapons-test values in order to remove the effect of the added flux of bomb- produced 14C from the data. The large input of artificially produced 14C began to make a significant imprint on the vertical profile of 14C concentrations sometime after 1959 and was particularly evident in data from the northwest Pacific Ocean by 1965. The observed temporal change in the vertical distribution of 14C, particularly the progressive downward penetration of the new input, can be used to provide additional estimates of some of the physical advec- tive and diffusive parameters. Figure 29 shows observed vertical profiles of 14C con- centration taken in the northeast Pacific Ocean in October 1959, in June 1965, and in October 1966. Some additional observations made in August 1964 below a depth of 200 m are also shown in the figure. The curve for October 10, 1959, is drawn through observations made by G. S. Bien, Scripps Institution of Oceanography, at30°04'N, 118°02'W. (Note that the range of uncertainty in the measurements is indicated for each observed point.) Observations also made by G. S. Bien at 49°00'N, 154°58'W, in August 1964 at depths of 210 m, 500 m, and 1,000m indicate remarkable uniformity in time and space. Evidently, the additional flux Cs. pC1/1001 40 50 400 FIGURE 28 Cesium-137 in pCi/100 liters; average of 10 vertical prof iles taken along 39° N, between 134° 15'Wand 134°59'W, by Robertson and Perkins, February 12, 1966. of bomb-produced 14C had not penetrated to 210 m by August 1964. The curve for June 30, 1965, is drawn through observa- tions made by A. W. Fairhall, University of Washington, at 48°29'N, 133°09'W. This curve shows that between October 1959 and June 1965 the influx through the surface of bomb- produced 14C had significantly increased the 14C concen- trations above about 200 m. This curve joins the curve drawn through the observations made in October 1959 at a depth of about 240 m. The curve for October 18, 1966, was drawn through observations also made by A. W. Fairhall, at 47°00'N, 132°03'W. This curve shows the further increase in the near-surface 14C concentration resulting from the in- crease of flux through the surface and also shows penetra- tion to a greater depth. This curve joins that of October 1959 at a depth of 300m. For the region below 300 m, a single curve has been drawn, since for the most part the observations made in the several locations and at the several times do not show statis- tically significant differences at any depths. The original data were given as 814C values, expressed as per-mille differences from a reference standard, and showed both positive and negative differences from the standard. For convenience in the numerical treatment of the data described below, we have here introduced an arbitrary zero

Physical Processes of Water Movement and Mixing 127 100- 200- 300- 400- 500- 600- 700 800 900 1000 Corbon-14 (Arb*trary Sea1e) 10 M 18 22 26 30 34 38 4^46 ^0 3? X ^ 6 S B1en, 30*04'N, IIB'02'W 0etober 10, I959 cw OS B*en, 49-OO N, I54°58' W August 16, 1964 h»-l AW Fo*rholi.48°29'N, I33°O9'W June 30, I965 m AWFo1rholi,47cOO'N, 132-03'W 0etober 18, 1966 I I I I I L FIGURE 29 Carbon-14 concentration (arbitrary units) with depth, northeast Pacific Ocean. shift so that all 14C "concentrations" appear as positive numbers. As stated above, 814C is expressed as a per-mille difference from a standard; however, in the following treat- ment of these data, the absolute values of the concentration ultimately cancel out of the problem. Hence, for conven- ience in keeping track of units, we have here considered that the zero-shifted per-mille values for 614C represent a concentration of 14C in arbitrary units per cubic meter, expressed as F/m3 (F being an undefined unit of mass). Assume that in the region of the ocean in which these 14C data were obtained, and for the time scale being con- sidered, the vertical variations in concentration, and particu- larly the time changes in the vertical distribution, are con- trolled by the physical processes of vertical flux. Specifically, for the time period represented by the 1965 and 1966 data, it is assumed that data relating to the horizontal advective and diffusive processes are not important in determining the vertical variation in concentration. Under these assumptions, we have, for a given time and depth, 9z 3z a / d? — { ** — I . (38) where f = concentration of 14C z = vertical coordinate, positive downwards w = vertical velocity Kz = vertical diffusivity If this equation is integrated from the surface to the depth z, we have (39) The surface limits on the right-hand side of this equation represent simply the flux of 14C through thfe surface, here designated by q0. Thus, we have i Jlr r at (40) by The left-hand side of this equation can be approximated * z (Kdz, = ± r „ dt Af J where f, represents the 14C concentration from the June 30, 1965, profile, and f2 represents the 14C concentration from the October 18, 1966, profile. Then, Af = r2 - tl = 475 days, or 4.11 X 1011 sec. Equation (40) then becomes, on re- arranging the order of terms, A/ - Kz z - f Af = q0 At - (f2 -?,) dz' . (42) The term q0 At represents the total flux through the sur- face during the time interval Ar. It is evident from the verti- cal profiles of 14C concentration for 1959, 1965, and 1966 that the added bomb-derived flux across the surface con- siderably exceeded the flux of natural radiocarbon. It is also evident that the bomb-produced 14C added to the surface layers of the ocean had not penetrated below 300 m in this area of the northeast Pacific as of October 1966. Therefore,

128 Radioactivity in the Marine Environment TABLE 8 Values of the Vertical Velocity, w, and the Vertical Coefficient of Eddy Diffusivity, Kz, Computed Using the Vertical Profiles of 14C Concentration Shown in Figure 29 (Values of the pertinent parameters entering the equations also given)0 8f z q0kt - 2 (?2~?i)Az o Depth (m) f -A — , Mj, -w (10-7m/sec) (plSi (F/m3) (106F/m4/sec) (109F/m3/sec) (cm2/sec) 0 46.4 - 1.91 1,542 0 0 _- 20 46.35 0.10 1.91 1,437 0.3 53 149 40 46.3 0.77 1.90 1,330 0.6 107 18.6 60 45.6 2.37 1.87 1,217 0.8 157 5.8 80 44.0 4.02 1.81 1,094 1.1 203 3.2 100 41.7 5.87 1.72 971 1.4 240 3.1 150 32.7 7.06 1.34 606 2.1 272 .2 200 25.9 4.12 1.06 262 2.1 224 .2 250 22.4 2.11 0.92 73 2.1 193 .2 300 20.3 1.44 0.84 0 2.1 175 .2 400 17.7 0.97 0.73 0 2.1 153 .6 500 15.5 0.90 0.64 0 2.1 134 1.5 600 13.5 0.62 0.56 0 2.1 117 1.9 700 12.5 0.29 0.51 0 2.1 107 3.7 800 11.9 0.25 0.49 0 2.1 103 4.1 1,000 11.0 0.16 0.45 0 2.1 95 6.0 "For symbols, assumptions, and method of computation, see text. q0 At is given approximately by the net change in accumu- lated 14C above a depth of 300 m—that is, given in Figure 29 can be used in Eq. (42) to find the verti- cal velocity, w, and the diffusivity, Kz. The procedure in- 300 = J (43) Note that, on the time scale considered here, the radioactive decay of 14C, which would contribute a term to the equa- tion having opposite sign to the flux of naturally produced 14C, has also been neglected. The vertical velocity, w, will be zero at the surface and would be expected to increase in magnitude with depth. Below 300 m, the right-hand side of Eq. (42) will be zero. Since the concentration decreases with depth, the balance required by Eq. (42) gives an upward-directed vertical veloc- ity, at least to a depth of 1,000 m. Since the horizontal mo- tion that must carry the adcending water back to regions of sinking is concentrated most strongly in the upper 200 m, we assume for our immediate purpose that the vertical velocity is constant from a depth of 1,000 m up to a depth of 150 m, and then decreases in magnitude to zero at the surface. The vertical density gradient in this region is approxi- mately constant through the depth range of 160 to 300 m, and the vertical diffusivity might also be expected to be constant through the same depth range. Making this assump- tion, data derived from the profiles of 14C concentration volved inserting into Eq. (43) the values of (fA/), / — Af 1 , \9z / z and q0&t - (f2-f ,) dz', corresponding to 160-m depth o and to 300-m depth. The resulting two simultaneous equa- tions are then solved for w and Kz. Values of (?2-?i) were obtained directly from the profiles for June 30, 1965, and October 18, 1966, while values off and 3f/9z, which enter the advective and diffusive flux terms, were determined from a slightly smoothed profile representing the average ?i andf2. The values of vertical velocity and diffusivity thus ob- tained were w = -2.1 X 10~s cm/sec (i.e., directed upward) and Kz = 1.22 cm2/sec. Taking w to be constant at this value throughout depth interval of 150 m to 1,000 m and then to decrease linearly in magnitude to zero at the surface, Eq. (42) can be used to obtain values for Kz at all depths from just below the surface to 1,000 m. Table 8 shows the values of the pertinent parameters obtained from the pro- files of 14C concentrations given in Figure 29, and the com- puted values of Kz This table shows that the computed values of Kz are essentially constant over the depth interval 160 to 300 m, supporting the assumptions that allowed the equation to be solved for both w and Kz.

Physical Processes of Water Movement and Mixing 129 The high value, of 149 cm2/sec, for the vertical diffusiv- ith at a depth of 20 m, shown in Table 8, indicates the rapid mixing above 50 m within the surface layer in this area of the oceans. The computed magnitudes of the vertical veloc- ity, of approximately 2 X 10~5 cm/sec, and of Kz in the thermocline, of approximately 1 cm2/sec, are consistent with a relatively long residence time for the waters below 1,000 m in the Pacific Ocean. Though Kz increases slowly with depth below 400 m, reaching a value of 6 cm2/sec at 1,000 m, the computations here do not support the work of Miyake et al. (1962); they are more in line with those of Munk (1966), as discussed in the previous section of this chapter. NEAR-SHORE AND ESTUARINE ENVIRONMENTS Man's most intimate contact with the marine environment occurs near the coast and in estuaries and other embay- ments, and he makes the most intensive use of this segment of the environment for the harvest of seafood and nonliving resources and for waste disposal. Consequently, it is to be expected that some radioactive materials from man's peace- ful uses of nuclear energy will enter the near-shore and estuarine waters; it is necessary to ensure that man's use of these waters and their products will not be limited by the introduction of these radioactive materials. Knowledge of the physical processes of movement and turbulent diffusion in estuaries has grown significantly in the last 15 or 20 years. The effort expended in study of the near-shore waters along the open ocean has, however, been relatively small. The region from just outside the surf zone to 20 or so miles offshore remains poorly understood, al- though the use of this near-shore environment as a receiver of man's unwanted waste materials is likely to increase greatly in the near future. Two reports have been published by the National Acad- emy of Sciences-National Research Council dealing with the disposal of low-level radioactive waste in coastal waters. These reports were written by working groups of the Com- mittee on Oceanography and for the most part treat the subject of the disposal of packaged waste into designated disposal areas. The first of these, Radioactive Waste Disposal into Atlantic and Gulf Coastal Waters (National Academy of Sciences-National Research Council, 1959), was prepared by a working group under the chairmanship of Dayton E. Carritt. The second, Disposal of Low-Level Radioactive Wastes into Pacific Coastal Waters (National Academy of Sciences-National Research Council, 1962), was prepared by a working group under the chairmanship of John D. Isaacs. Despite the emphasis on packaged-waste disposal, a problem of little current concern, these reports still con- tain considerable information about the physical and bio- logical character of coastal waters that can be used in con- sidering the probable environmental consequences of other possible sources of radioactive materials in these waters. The term near-shore zone is used here to designate the strip of water adjacent to the shoreline in which the adja- cent land boundary, freshwater runoff from the land, and local meteorological conditions contribute significantly to the physical processes of movement and mixing. The width of this zone is highly variable, and the outer boundary is not well defined. The near-shore zone may be quite narrow along coasts where the continental shelf is narrow and where oceanic conditions in which the motion of the water is dominated by the "permanent" currents, discussed earlier in this chapter, penetrate close to shore. Conversely, off a coast where the continental shelf is quite wide, the near- shore zone may be several tens of miles wide. The near-shore zone is not, however, coincident with the continental shelf. Where the shelf is very narrow, the near-shore zone may ex- tend beyond the shelf, and where the shelf is very wide, the near-shore zone may extend out from shore for only a frac- tion of the shelf width. The critical features defining this zone are the dominance of boundary effects and of transient local effects on the water movement. There is considerable temporal and spatial variation in the movement of the waters in the near-shore zone. Except near inlets, the tidal component of the motion is generally parallel to the coast and oscillatory in character, with the onshore-offshore component increasing with distance from the coast. Inshore from the point where surface waves are breaking—that is, in the surf zone—a longshore current usu- ally develops in a direction dependent upon the angle at which the waves approach the shoreline. Thus, along a coast- line oriented in a north-south direction, with the ocean to the east, waves approaching the shoreline from the north- east will produce a longshore current that flows southward. Outside the surf zone, the local wind and the salinity gradi- ent, which is related to runoff from the land, combine to dominate the nontidal current in the near-shore zone. Since the waves breaking on a shoreline at any given time may have been for the most part generated by storm systems some distance away, the direction from which the waves approach the coast and the local wind direction are gener- ally not correlated. Consequently, the direction of flow in- side the surf zone may be opposite to the direction of the currents seaward of the surf zone. Along coasts having relatively large freshwater inflows to the ocean, such as the Atlantic coast of the United States, the salinity, and hence the density, of the water increases with distance offshore. The average net nontidal flow in the near-shore zone will, along such coasts in the northern hemi- sphere, be directed such that the shoreline is to the right of an observer looking downstream. Such currents are particu- larly well developed along coasts to the right (looking sea-

130 Radioactivity in the Marine Environment ward) of the mouths of major estuaries-southward from the mouth of the Chesapeake Bay, for example. At any particular time, however, the currents in the near- shore zone may be dominated by the local wind or by density-induced effects resulting from the wind. In the shallow waters characteristic of the near-shore zone, the direct, wind-induced transport of the near-surface waters is directed slightly to the right of the wind. Hence, an offshore wind will transport the surface waters offshore, particularly a wind blowing at an angle to the shoreline such that an observer with his back to the wind has the shoreline on his left hand. If this occurs at a time of the year when there is a vertical density gradient with warmer waters at the surface, these warmer waters are transported offshore and the cooler waters from offshore are transported along the bottom and well up along the shoreline. The resulting density distribu- tion will produce, in the northern hemisphere, a current flowing along the coastline with the shore to the left of the current (looking downstream). When such an offshore or longshore wind ceases, the warmer surface layers slosh back toward the shore. Dye- tracer studies along open coastlines have shown that in this way pollutants introduced from an offshore outfall are most likely to be carried onto the beach following the cessation of a wind that has produced an offshore surface-layer trans- port. In the presence of an onshore wind, on the other hand, a slope zone develops near the shore and the wind-induced transport turns and runs parallel to the shoreline at a point just outside the breaker zone. Radioactive materials introduced into the near-shore zone will be transported away from the point of discharge by the current present in the vicinity of the discharge at the time of discharge, and will be mixed into the receiving wa- ters by turbulent diffusion. Where there is continuous dis- charge of radioactive materials into the near-shore zone, a diverging plume extending downcurrent from the source will develop, with concentration levels in the plume decreas- ing with distance from the source. Because of the transient character of the current pattern in the near-shore zone, the plume will show temporal variations in direction, some- times folding back on itself, but more often, when the cur- rent direction approximately reverses, the remnants of the older, lower concentration plume will be advected along a path somewhat offset from the path of the new plume ex- tending from the source in the new direction of the current. Over a long period of time, a general low-level concentra- tion field will be built up in the vicinity of the source, upon which the transient, higher concentration plume is superim- posed. The steady-state level of this general background concentration will depend upon the rate at which the waters of the near-shore zone are exchanged with waters of the ad- jacent outer shelf or oceanic region. We have but meager knowledge of these exchange pro- cesses by which the waters of the near-shore are renewed. Where the inflow of fresh water from the land into the near- shore zone is sufficient to produce measurable salinity gra- dients, and where the rates of freshwater inflow can be determined, the mean residence time for the water of the near-shore zone can be estimated. Such an estimate was made by Ketchum and Keen (1955) for the waters of the entire continental shelf along the Atlantic coast of the United States between Cape Hatteras and Cape Cod. Assuming that the source of the water that exchanges with the waters over this segment of the continental shelf is the "slope water," which is formed between the Gulf Stream and the continental shelf, these investigators used the ob- served salinity distribution to compute the total volume of river water resident over the shelf. Dividing this accumula- tion of water derived from land drainage by the annual vol- ume rate of flow from all rivers discharging from the adja- cent coast gave a mean residence time for this segment of the continental shelf of about 1!£ years. Conceivably, this approach could be modified to apply to any segment of the near-shore zone along this coastline or any other coastline where similar conditions of freshwater inflow prevail. Along coastlines where freshwater drainage from land is too small to develop measurable salinity variations, the use of some other tracer, either natural or artificial, will be re- quired in order to determine the exchange rates between the waters of the near-shore zone and waters of the adjacent outer continental shelf or open ocean. As stated earlier, estuary studies during about the last 15 years have been rather extensive, and a considerable volume of literature has been published concerning the distribution of properties and the circulation patterns in the various types of estuaries. Cameron and Pritchard (1963) contrib- uted a review of this literature, which also contains a rep- resentative list of references concerned with estuaries through about 1960. The book entitled Estuaries (Lauff, 1967), published by the American Association for the Ad- vancement of Science in 1967, refers to several more recent papers dealing with the kinematics and dynamics of estu- aries. Other references that treat studies of this subject in- clude those of Rattray and Hansen (1962), Hansen and Rattray (1965, 1966), and Pritchard (1955). An estuary has been defined (Pritchard, 1967a) as a semi- enclosed coastal body of water that has a free connection with the open sea and within which seawater is measurably diluted with fresh water derived from land drainage. From a geomorphological standpoint, four primary subdivisions of estuaries are recognized: drowned river valleys, fjord-type estuaries, bar-built estuaries, and estuaries produced by tec- tonic processes. Drowned river valleys are the classical estuaries of the physical geographer. Because they are generally confined to coastlines with relatively wide coastal plains, these water- ways have also been called coastal-plain estuaries. These estuaries are widespread throughout the world, and are

Physical Processes of Water Movement and Mixing 131 common along the eastern seaboard of the United States. This class of estuaries has also been studied the most, and most of the existing literature about estuaries deals with them. Coastal-plain estuaries may be further subdivided into four principal types (Pritchard, 1955, 1967b), differing from one another in the character of the nontidal circula- tion pattern, in the intensity of vertical stratification, and in the extent of lateral homogeneity. These types are the salt-wedge estuary, typified by the mouth of the Mississippi River; the partially mixed estuary, typified by the Chesa- peake Bay and its tributary estuaries; the vertically homog- eneous estuary; and the sectionally homogeneous estuary. Most estuaries fall into the category of partially mixed estuaries, and further discussion here will therefore be lim- ited to this type. This discussion of the movement and mix- ing in partially mixed coastal-plain estuaries covers the processes of importance in estuaries in general and makes adequate reference to the literature dealing with other categories of estuaries. In a partially mixed estuary, the salinity increases with depth as well as in the seaward direction. There is usually a surface layer in which the vertical salinity gradient is small, an intermediate layer in which the salinity increases rela- tively rapidly with depth, and a deep layer in which the rate of increase of salinity with depth is small, as in the surface layer. While the intermediate layer is one of relatively high stability, the density gradient is not sufficiently steep to completely inhibit vertical mixing between the surface layer and the bottom layer. The oscillatory ebb and flood of the tide are the predomi- nant motions in the estuary. Superimposed on the tidal cur- rents is a net circulation pattern in which there is a net sea- ward flow in the surface layers and a net flow from the mouth toward the head of the estuary in the deeper layers. There is also a small net vertical motion from the deeper layers to the surface layers. The volume of water flowing toward the head of the estuary per unit time decreases from the mouth to the head of the estuary, since water is simul- taneously being transferred through vertical motion from the deeper layers to the surface layers. Hence, the volume rate of seaward flow in the surface layers increases from the head toward the mouth of the estuary. A pollutant initially introduced into the bottom layers in a partially mixed coastal-plain estuary, in addition to par- ticipating in the oscillatory movement of the tidal currents, is carried in the net motion toward the head of the estuary. At the same time, turbulent mixing leads to horizontal dis- persion in the longitudinal and lateral directions and to verti- cal dispersion into the surface layers. Pollutant that becomes mixed with the surface layers is carried in the net flow to- ward the mouth. Seaward from the point of introduction, pollutant being carried toward the ocean in the surface layers is partially mixed downward into the deeper layer and reintroduced into layers moving toward the head of the estuary. A pollutant introduced into the surface layers is initially carried in the net flow toward the mouth of the estuary. Mixing leads to horizontal and vertical spreading, and the wastes are thus added to the deeper layers, which have a net flow toward the head of the estuary. In the region of the estuary headward from the point of introduction, the concentrations of pollutant will always be greater in the deeper layers than in the surface layers, while seaward from the point of introduction the converse will be true. These conditions prevail regardless of whether the wastes are initially introduced into the surface layers or into the deeper layers. The pollutant is ultimately flushed from the estuary in the seaward flow of the surface layers. In order to understand these various processes in greater detail, consider a waste effluent introduced via an outfall into the estuary. The subsequent fate of the introduced pol- lutant will be influenced by the physical properties of the effluent, the method of introduction, and the depth of in- troduction. If the density of the effluent stream is lower than that of the receiving waters, and the stream is intro- duced at the surface of the estuary, then vertical mixing of the waste materials with the receiving waters will be inhib- ited. However, if such a waste stream is introduced into the estuary near the bottom, the effluent will initially rise as a buoyant plume, entraining diluting water from the environ- ment en route to the surface. Since the estuary is seldom deep enough that the ascending plume reaches the density of the receiving waters at an intermediate depth, the plume, still somewhat lower in density than the surrounding estu- arine waters, will spread out on the surface. If the waste effluent is denser than the estuarine waters, the waste stream will tend to spread out on the bottom. Ini- tial mechanical dilution can be enhanced in this case by in- troduction of the waste stream near the surface, thus provid- ing for a descending plume that will entrain diluting water en route to the bottom. The major sources of pollution to an estuary are usually introduced by way of effluent streams that are less dense than the receiving waters, and as noted above, the most effective way to introduce such a waste stream would be as a bottom discharge. The effectiveness of the dilution of the ascending plume is enhanced by discharging the waste stream through a multiport diffuser, designed so that the ascending plumes overlap slightly when they reach the sur- face. This method produces an elongated volume source in the surface waters, which is then further subjected to the physical processes of movement and dispersion in the estuary. In some situations, the volume rate of discharge of the effluent stream is so great that little mechanical dilution can be obtained from a rising plume in the depth range available

132 Radioactivity in the Marine Environment in the estuary without a complex and costly diffuser system. An alternative method of obtaining effective initial mechani- cal dilution is to introduce the waste stream as a high-velocity jet directed across the waterway. If the method of introduction produces sufficient initial mechanical dilution to significantly reduce the density dif- ference between the waste stream and the estuarine waters, further dilution by mixing is enhanced. In the surface layers, the diluted effluent will be ex- tended into an elongated horizontal plume by the prevailing tidal currents. During ebb tide, the plume will extend down the estuary, and during flood tide the plume will extend up the estuary. Horizontal and vertical turbulent diffusion will act along the length of the plume to spread the waste ma- terials and to continually reduce the contaminant concen- tration with distance from the source. Each reversal of the tidal current will result in a folding back of the spreading plume. However, because of the large-scale turbulent eddies, the plume will seldom fold exactly back on itself and will also seldom follow the same path on successive tides. Thus, there will develop a widespread contaminant field of rela- tively low concentration, on which is superimposed, with each tide, a relatively narrow plume of higher concentration. Tidal oscillations past irregularities in the shoreline are an important mechanism in the longitudinal dispersion of an introduced pollutant. This is made most evident by con- sidering a contaminated volume, produced by an instantane- ous release, as it is carried up and down the waterway by the tidal currents. Frequently, eddies associated with slight embayments or with points of land that project into the waterway will temporarily trap water containing high con- centrations of pollutant as the contaminated volume moves past these shore features on one or the other phase of the tide. The main bulk of the contaminant is carried on past the shore feature by the tidal current, while the material trapped by the shore feature slowly spreads out into the main stream, leading to an effective dispersal behind the bulk of the contaminated volume. When the tide reverses, the process is repeated, with a resulting dispersion on the opposite side of the contaminated volume. The theoretical treatment of mixing discussed earlier in this chapter can be modified to treat the distribution of concentration of a pollutant discharged into an estuary either as a local nearly instantaneous source or as a local continuous source. The modification includes the effects of the side boundaries and of the boundary conditions assumed at the river and seaward ends of the estuary. Determination of the probable time-dependent distribution in a plume orig- inating from a continuous source requires further considera- tion of the oscillatory nature of the tidal current. Carter (1965) has described a theoretical approach that appears to satisfy many of the observed features of the oscillating plume in a tidal estuary. The use of theoretical relationships for mixing appear to be most useful in describing the detailed distribution of pol- lutant concentration within, for example, a tidal segment of an estuary (i.e., the segment defined by the excursion from its source of a particle of water in an estuary, headward on the flood tide and seaward on the ebb tide). A number of investigators have, on the other hand, treated the broader aspects of the flushing of an estuary. In such studies, con- cern is directed toward the broad mechanisms of the move- ment of the pollutant through the estuary and of its ultimate discharge to the open ocean. Ketchum (1950), Stommel (1953), Kent (1958), and Dorrestein (1960) all treat the flushing of estuaries as a one-dimensional (longitudinal) problem. Stommel and Kent deal with solutions to the one- dimensional advection-diffusion differential equation, while Ketchum and Dorrestein use a finite, segmented ap- proach, sometimes referred to as a box model. More recently, Pritchard (1969) described a two-dimen- sional box model that is particularly suited to partially mixed estuaries. In this approach, the estuary is divided into segments along the length of the estuary, and each such longitudinal segment is further subdivided vertically at the depth of the maximum vertical salinity gradient, which approximately defines the boundary between the net non- tidal seaward-flowing upper layer and the deeper layer in which the flow is directed headward in the estuary. Using volume and salt continuity requirements for each segment, a series of simultaneous equations is developed from which the larger scale advective flows and vertical-exchange coef- ficients can be determined. It is theoretically possible to obtain numerical solutions to the basic hydrodynamic and kinematic equations using high-speed computers. These equations are so complex that to date it has not been possible to treat the complete transient-state equations with even the largest of high-speed computers. However, numerical modeling of estuarine circu- lation, and of the distribution of salinity and introduced wastes, using models of considerably greater complexity than have been employed where analytical solutions were sought, is developing rapidly. In numerical modeling of estuaries, the equations of mo- tion are used to determine both the mean circulation and the tidal flow. To date, the Navier-Stokes form of the equa- tions of motion, in which the local and field acceleration terms are neglected, has been used for the mean flow, and the classical wave equations for the computations of tidal flow, using the rise and fall of the tide at the entrance as input. The continuity equations for mass and salt must be solved simultaneously with the equations of motion to pre- dict the temporal and spatial distribution of both the circu- lation and the salinity. Prediction of the distribution of concentration of a waste requires the simultaneous solution of the convective-diffusion equations and the equations of motion. In all cases to date, the equations employed in the numer-

Physical Processes of Water Movement and Mixing 133 ical model still represent considerable simplification of the complete hydrodynamic and kinematic equations. In partic- ular, transient-state solutions for the nontidal circulation will ultimately be required, although such has not been done to date. Also, to treat the majority of estuarine problems, the vertical dimension must be included, since the charac- teristic two-layered estuarine circulation dominates so many of the estuaries in this country. The greatest problem with numerical modeling of the estuary is that the relationships between the diffusion pa- rameters that enter the equations and predictor variables such as tide, weather, and circulation are not known. There are two schools of thought on how to overcome this prob- lem. One contends that if the field of motion is determined in sufficient detail in space and time, the diffusion terms become relatively unimportant, and only rough estimates of the diffusion parameters are required. The second school advocates determining the pertinent relationships by which the diffusion parameters applicable to any desired averaging scale can be computed. The advantage of the first approach is that at least two-dimensional modeling is possible now, though at considerable cost in computer time, since very short intervals in time and space are involved. The advantage of the second approach is that, for situations requiring much less detail in time and space, less computer memory and computer time is required, and the possibility of extending the model to three spatial dimensions appears more favor- able. Hydraulic models of estuaries have been and are being used to study the physical dispersion of proposed waste dis- charges. A hydraulic model is inherently three-dimensional, and time variations in tidal input and freshwater inflow are readily included in the model. Properly verified hydraulic models of estuaries are capable of producing valid informa- tion on the physical dispersion of waste materials introduced into the estuary at intermediate and large scales of averag- ing. There is some indication that the details of concentra- tion distribution near the point of discharge may not be properly scaled in the model as a result of overmixing at small scales, which is associated with the roughness elements required for distorted hydraulic models. Simmons and Lindner (1965) discuss the uses of hydraulic models of tidal waterways, and Ippen (1966) shows that while dispersion phenomena in such models are properly scaled in the salt- water section, there are questions regarding the scaling of such phenomena in the freshwater tidal-river section. The latter report also contains a chapter on the general scaling requirements for hydraulic models of estuaries. It is doubtful that the costs of construction of a hydrau- lic model of an estuary can be justified on the basis of waste management alone; however, the use of existing hydraulic models, built for other purposes, does appear feasible. This is particularly true for problems where all three spatial dimensions are important, since proven alternative means of solution are not yet available. SUMMARY In this chapter the physical processes that result in move- ment and mixing of radioactive materials within the ocean are described. The current state of our knowledge of the essential features of the circulation of the oceans in relation to the associated distribution of properties is summarized, and recent theoretical studies of ocean circulation are reviewed. Considerable progress has been made over the last ten years in understanding the processes of mixing in the ocean and in adjacent coastal and estuarine waters. Consequently, a major portion of this chapter is devoted to a description of our current knowledge of turbulent diffusion in the ocean. Comparisons between experimental and theoretical results are also given. Some oceanographic implications of the observed dis- tribution of natural tracers, such as carbon-14, and of fall- out isotopes, are discussed. Particular attention is given to the conflicting evidence concerning the rate of vertical pene- tration of the dynamically passive isotopes strontium-90 and cesium-137, discussed elsewhere in this publication. Variations of carbon-14 with depth in the interval 1959 through 1966 at a location in the northeast Pacific Ocean are used to compute the vertical components of the mean velocity and of the eddy diffusivity. The results of this analysis are in line with those of Munk (1960), and con- trary to the conclusions reached by Miyake et al. (1962). Because man's most intimate contact with the marine environment occurs in coastal areas and in estuaries and other embayments, a section of this chapter is devoted to a brief description of the processes of movement and mixing in these waters. References are given to several recent papers containing more detailed descriptions of the state of our knowledge of the physical processes in estuaries and other coastal waterways. REFERENCES Bodman, R. H., L. V. Slabaugh, and V. T. Bowen. 1961. A multi- purpose large volume sea-water sampler. J. Mar. Res. 19(3):141- 148. Unlit*. B, and H. Stommel. 1961. On the abyssal circulation of the World Ocean-IV. Origin and rate of circulation of deep ocean water as determined with the aid of tracers. Deep-Sea Res. 8:95-110. Bowden, K. F. 1964. Turbulence. Annu. Rev. Oceanogr. Mar. Biol. 2:11-30. Bowden, K. F. 1965. 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136 Radioactivity in the Marine Environment state of knowledge of factors affecting tidal hydraulics and re- lated phenomena. Rep. No. 3. Committee on Tidal Hydraulics, Corps of Engineers, U. S. Army, Vicksburg, Miss. Somerville, B. T., and A. F. B. Woodhouse. 1950. Ocean passages for the world. 2nd ed. Admiralty Hydrogr. Dep., London. Stalcup, M. C., and W. G. Metcalf. 1966. Direct measurements of the Atlantic Equatorial undercurrent. J. Mar. Res. 24(1):44-5S. Stommel, H. 1949. Horizontal diffusion due to oceanic turbulence. J. Mar. Res. 8(3):199-225. Stommel, H. 1953. Computation of pollution in a vertically mixed estuary. Sewage Ind. Wastes 25(9):1065-1071. Stommel, H. 1955. The anatomy of the Atlantic. Sci. Amer. 191(1): 2-7. Stommel, H. 1957. A survey of ocean current theory. Deep-Sea Res. 4:149-184. Stommel, H. 1963. Varieties of oceanographical experience. Science 139:572-575. Stommel, H. 1965. The Gulf Stream, a physical and dynamical de- scription. 2nd ed. University of California Press, Berkeley, Calif. Stommel, H., and A. B. Arons. 1960a. On the abyssal circulation of the World Ocean-I. Stationary planetary flow patterns on a sphere. Deep-Sea Res. 6:140-154. Stommel, H., and A. B. Arons. 1960b. On the abyssal circulation of the World Ocean-II. An idealized model of the circulation pat- tern and amplitude in oceanic basins. Deep-Sea Res. 6:217-233. Sverdrup, H. U. 1947. Wind-driven currents in a baroclinic ocean; with application to the equatorial currents of the eastern Pacific. Proc. Nat. Acad. Sci. U. S. 33:318-326. Sverdrup, H. U., M. W. Johnson, and R. H. Fleming. 1942. The oceans; their physics, chemistry and general biology. Prentice- Hall, New York. Swallow, J. C. 1955. A neutral-buoyancy float for measuring deeo currents. Deep-Sea Res. 3:74-81. Swallow, J. C., and L. V. Worthington. 1961. An observation of a deep countercurrent in the western North Atlantic. Deep-Sea Res. Taylor, G. I. 1953. Dispersion of soluble matter in solvent flowing slowly through a tube. Roy. Soc. (London), Proc., A. 219:186- 203. Taylor, G. I. 1954. The dispersion of matter in turbulent flow through a pipe, Roy. Soc. (London), Proc., A. 223:446-468. Volkmann, G. H. 1962. Deep current observations in the western North Atlantic. Deep-Sea Res. 9:493-500. Volkmann, G. H., J. A. Knauss, and A. C. Vine. 1956. The use of parachute drogues in the measurement of subsurface currents. Amer. Geophys. Union, Trans. 37(5):573-577. Warren, B. A. 1963. Topographic influences on the path of the Gulf Stream. Tellus 15:167-183. Webster, F. 1963. A preliminary analysis of some Richardson cur- rent meter records. Deep-Sea Res. 10:389-396. Webster, F. 1965. Measurements of eddy fluxes of momentum in the surface layer of the Gulf Stream. Tellus 17:239-245. Wooster, W. S., and G. H. Volkmann. 1 960. Indications of deep Pacific circulation from the distribution of properties at five kilometers. J. Geophys. Res. 65 (4): 1239-1 249. Wust, G. 1935. Die Stratosphare des Atlantischen Ozeans. Deutsche Atlantische Expedition, METEOR, 1925-27. Wiss. Erg., Bd. 6, 1, Teil, Lief 2. Wust, G. 1949. Die Kreislaufe der atlantischen Wassermassen, ein neuer Versuch raumlicher Darstellung. Forsch. Fortschr. 25 (23/24): 28 7-290. Wust, G. 1964. Major deep-sea expeditions and research vessels 1873-1960, p. 1-52. In M. Sears [ed.] , Progress in oceanog- raphy. Vol. 2. Pergamon Press, New York.

Chapter Five MARINE CHEMISTRY E. D. Goldberg, W. S. Broecker, M. G. Gross, K. K. Turekian INTRODUCTION Chemical species introduced into the oceans will initially be partitioned among three phases: the living biosphere, sea- water, and inorganic and organic particles. On different time scales and in various sites, the ultimate fate of all such ele- ments is removal to the sea floor or discharge into the atmo- sphere. Although it is not possible to treat in detail the paths of all chemical species in the various types of marine environments, we can attempt to systematize available chemical data for radionuclides in seawater and in sedi- ments and to direct attention to those areas where informa- tion is lacking. Marine environments can be conveniently categorized into two major domains: the coastal ocean and the open ocean. The coastal ocean includes estuaries, lagoons, the water over the continental shelves, and many marginal seas. The open ocean is that part not significantly affected by its boundaries with the continents or by the shallow-ocean bottom. Obviously, there is no clear-cut boundary between the coastal and open ocean; therefore, for this report, we will consider water deeper than 1,000 m to be part of the open ocean. The different physical and biological conditions of these two oceanic domains, relevant to problems of elemental dis- tribution, are summarized in Table 1. The remainder of the chapter elaborates on these concepts. CHEMICAL SYSTEMATICS AND ELEMENTAL REACTIVITIES IN SEAWATER The formulation of models to study the dispersion of radio- active species introduced into the marine environment can be approached within the framework of chemical charac- teristics and the behaviors of their stable counterparts in seawater. The assumption is made that the dispersion paths of radionuclides introduced in soluble forms will be the same as those of stable nuclides introduced or existing in the marine environment. This implies that the chemical speciation is the same for both stable and radioactive nu- clides in seawater.* Hence, it is possible to utilize existing knowledge of oceanic chemistry in formulating models. The complexities of seawater as an electrolyte solution and the inadequacies in our quantitative description of the oceanic *There are evidences in the literature of exceptions to this assump- tion. For example, stable zinc appears to exist in a number of com- plex species, some of which exchange slowly with the uncomplexed forms. Zinc-65, introduced into the marine environment from nu- clear installations, may not attain the same chemical speciation in short time intervals as its stable isotopic counterparts. Some of the reported differences of specific activities between organisms and the water may result from the preferential uptake of a specific dissolved species of zinc. Another explanation may be that organisms may have picked up these elements from water masses where the specific activities were different but the speciation was similar. At present, resolution of this difficulty is not evident. 137

138 Radioactivity in the Marine Environment TABLE 1 Primary Factors That Can Alter the Chemical Composition of Seawater Factor Effect upon Elemental Behavior Coastal Ocean Open Ocean Primary productivity Particle input by river runoff, or resuspension from bottom Reservoirs for element accumulation Water circulation Fixation of elements in biomass, with subsequent transfer to deeper waters or to sediment Provide surfaces for reactions of dissolved species and sites for bacterial activity Storage of elements for various periods of time Dispersion or retention of introduced species High, with local variability High Exist in sediments of ocean bottom Partial retention near coast Generally low, except in areas of divergence and high latitude Low Exist in deep water and sedi- ments of ocean bottom Dispersion dominant system are well known. Substantial advances have been made in the chemical description of seawater over the past years, especially in regard to the speciation of the elements and to their relative reactivities. This new information per- mits meaningful statements about the expected behavior of at least some of the nuclides. Table 2 lists average values for the concentration of ele- ments in the ocean, together with what appears to be, from thermodynamic considerations, the most important chemi- cal form, or forms, in solution. Column 4 divides the vari- ability in the abundance of the elements into the following three categories. A. Concentration is directly proportional to the salinity (such elements are referred to as "conservative"). B. There is a well-developed and readily described vari- ability in concentration, as a function of depth, ocean basin, or both. C. Reported variations in abundance are independent of salinity and not clearly dependent on depth or oceanic basin. The elements in Class A are, in general, unreactive and display a remarkable stability in solution, while elements in Class B are usually involved in biological cycles, perhaps in inorganic processes that may result in an inhomogeneous oceanic distribution. The behavior of Class C elements in the ocean is not well understood. There are several approaches to the description of the reactivity of an element in the oceanic chemical system, the most useful of which are residence times and the degree of undersaturation or supersaturation. Residence time is defined as the average time an element spends in ocean water between introduction and incorpora- tion into the sediments. Reactive elements generally have relatively short residence times in the oceans, while chemi- cally inert species generally have much longer residence times, assuming a steady-state system in which the amount of an element entering the marine environment is compen- sated by the transfer of an equivalent amount from seawater to the sediments. The residence time, T, is defined by the relationship T = A/(dA/dt), where A is the total amount of the element in solution in the oceans and dA/dt is the amount introduced, and there- fore precipitating, per unit time. Table 2 gives values of the residence times based upon values of dA/dt calculated from stream-input data. Because of the oversimplified nature of the model, the absolute values of these residence times should be taken as a measure of reactivity rather than as a meaningful chrono- logical number. The alkali metals and the alkaline-earth metals, for example, with long residence times, are charac- terized by the lack of reactivity of their ions in solution, while those elements intimately involved in biological cycles-phosphorus and silicon—have short residence times (103 to 104 years). The shortest residence times are calcu- lated for elements primarily associated with lithogenous particles, such as aluminum, titanium, and thorium. A second measure of reactivity derives from the degrees of undersaturation of ions with respect to their least soluble compound and their most stable dissolved species. It has been noted that, for reactive elements whose expected con- centrations are calculated on the basis of their least soluble salts (Table 3) or on the basis of stable complexes (Table 4), and that are classified according to residence times (except for the rare earths and thorium), the observed concentra- tions are much lower than the limiting ones for oxygenated seawater. This indicates that phenomena other than solu-

Marine Chemistry 139 TABLE 2 Geochemical Characteristics of the Elements" Element Sea water Concentration (Mg/liter) Principal Dissolved Species Category6 Concentration Dissolved in Stream Waters (Mg/liter) Residence Time in Ocean (yr) H 1.1X108 H2O A __ He 7X10"3 He (gas) A — - Li 1.7X102 Li•1• A 3 2.3 X106 Be 6X10^ - - - - B 4.5 X103 B(OH)3,B(OH)^ A 10 1.8 X107 C 2.8 X104 HCOj, CO],2 A - - C (org.) 1X102 - A - - N 1.5 X104 N2 (gas) A - - N 6.7X102 NOj B - - 0 8.8 X108 H20 A - - 0 6X103 °2 B - - 0 .8X106 so;2 A — - F .3X103 F~ A 100 5.2X10s Ne 0.12 Ne(gas) A - 6.8 X107 - Na .1X107 Na+ A 6,300 Mg .3X106 Mg+2 A 4,100 1.2X107 Al — — 400 1.0X102 Si 3X103 Si(OH)4, SiO(OH)3 B 6,500 1.8 X104 P 90 HPO42, H2PO4, PO43 B 20 1.8 X 10s S 9.0 X1 0s S042 A - 1X108 Cl 1.9X107 CT A 1,800 Ar 4.5 X102 Ar (gas) A — — K 3.9 X 10s K+ A 2,300 7X106 Ca 4.1 X 10s Ca+2 A 15,000 1.0X106 Sc <4X10-3 Sc(OH)? - 0.004 <4X104 Ti 1 Ti (OH);{ - 3 1.3X104 V 2 V02(OH)f - 0.9 8.0 X104 Cr 0.5 CrO42, Cr+3 - 1 2.0 X104 Mn 2 Mn'1•2 C 7 1.0X104 Fe 3 - - 670 2.0 X102 Co 0.4 Co+2 C 0.1 1.6 X 10s Ni 7 Ni+2 C 0.3 9.0 X104 Cu 3 Cu'1-2 C 7 2X104 Zn 10 Zn+2 C 20 2X104 Ga 3X10-2 - - 0.09 1X104 Ge 7X10-2 Ge(OH)4 - - 5X104 - As 2.6 HAsO*2, H7AsOT - 2 2X104 Se 9X10-2 SeO42 C 0.2 Br 6.7 X104 Br~ A 20 1X108 Kr 0.2 Kr (gas) A - 5X106 - Rb 1.2X102 Rb+ A 1 Sr 8X103 Sr+2 A 70 4X106 Y 1 X 10-3 Y(OH)§ C - - Zr 3X10-2 - - - - Mb 0.01 - - 7X105 - Mo 10 MoO42 A 0.6 Ru - - - — - Rh - — - - - Pd - - - - 4X104 - Ag Cd 0.3 AgCl2 Cd+2 C 0.3 0.1 In <20 — — - - Sn 0.8 - - - - Sb 0.3 - C 2 7,000 Te - - - - - I 60 103,1 A 7 4X10s Xe 5X10-2 Xe (gas) A - -

140 Radioactivity in the Marine Environment TABLE 2 (Continued) Sea water Concentration (Mg/Hter) Principal Dissolved Species Concentration Dissolved in Residence Stream Waters Time in Ocean (Mg/liter) (yr) Element Category* Cs 0.3 Cs+ A 0.02 6 X105 Ba 20 Ba+2 C 20 4 Xl04 La 3 X10"3 La (OH)o C 0.2 6 X102 Ce IX10"3 Ce (OH)? c -- Pr 0.6 X10-3 Pr (OH)? c - - Nd 3 X10-3 Nd (OH)? c _ - Sm 0.5 X10-3 Sm (OH)? c - - Eu 0.1 X10'3 Eu (OH)? < - - Gd 0.7 X10-3 Gd (OH)Q c - - Tb 1.4 X10-3 Tb (OH)? c - - Dy 0.9 X10"3 Dy (OH)° x c - - Ho 0.2 X10"3 Ho (OH)? c - — Er 0.9 X10-3 Er (OH)? c - - Tm 0.2 X10-3 Tm(OH)? c — - Yb 0.8 X10-3 Yb (OH)lj c - - Lu 0.1 X10"3 Lu (OH)§ c - - Hf <8X10-3 - - - Ta <3X10-3 - — - - W 0.1 WO^2 - 0.03 1.2X10s Re 0.008 - - - - Os - - - - - Ir - - - - Pt - - - - - Au IX10"2 AuClJ c 0.002 2 X105 Hg 0.2 HgClJ2, HgCl§ c 0.07 8 X104 Tl <0.1 Tl+ - - - Pb 0.03 PbClJ, PbCl+, Pb+2 c 3 4X102 Bi 0.02 - - - - Po - - - - - At - - - - - Rn 6 X10-13 Rn (gas) - - - Ra 1XI0-7 Ra+2 c - - Ac - — - — - Th <5X10-* Th(OH)2 - 0.1 <200 Pa 2.0 XI0"6 - - - — U 3 U02(C03)^ A 0.04 3 X106 "Compiled from Goldberg (1965) and Turekian (1969). 6See text for explanation of letters.

Marine Chemistry 141 TABLE 3 Expected Equilibrium Concentrations for Some Elements, Based on Insoluble Salts of Phosphate, Carbonate, Hydroxide, and Sulflde (Concentrations in log moles/liter)" P043 CO52 OH- S'2 (log a = -9) Observed in Seawater Element (log a = -9.3) (log a =-5. 3) (log a - -6) La+3 -11.1 - 0 - -10.7 Ce+3 -10.0 - - - -10.2 Th+4 -11.8 - - - -11.7 Cr+3 -11.3 - - - -8.06 uo}2 9.2 - — - -7.8c Fe+3 -10.6 - — — -7.3" Fe+2 - - — -6.4 -7.3d Mn+2 - -3.1 +0.2 -2.6 -7.4 Co+2 -4.4 -6.5 -2.2 -12.1 -8.2 Ni+2 -2.9 -0.6 -3.2 -10.7 -6.9 Cu+2 -5.1 -3.5 -5.8 -26.0 -7.3 Ag+1 -2.0 -2.7 -1.5 -19.8 -8.5s Zn+2 -3.5 -3.7 -3.5 -14.1 -6.8 Cd+2 -3.7 -5.0 -0.5 -16.2 -9.0 Hg+2 - - -12.5 -43.7 -9.1e Al+3 - - -12.0 — -8.3 Ga+3 - - -16.0 - -9.3 Sn+2 - - -15.0 -16.0 -8.2 Pb+2 -6.8 -6.8 -2.0 -16.6 -9.8e "Calculations made with the following activity coefficients: monovalent ions, 0.7; divalent ions, 0.1; trivalent ions, 0.01. 6Occurs primarily as CrO^2. cOccurs primarily as UO2(CO3)^*. "May occur as particulate phases. e Occurs primarily as chloride complexes. TABLE 4 Complexes Formed in Seawater and Their Expected and Observed Equilibrium Concentrations (in moles/liter) Element Complex Expected" Observed Silver AgClJ -4.2 -8.5 Mercury HgClJ HgCl0 +1.9J -03 J -9.1 Lead PbClJ -5,1 -5.8} PbCl+ -9 'Using least soluble salt, from Table 3. bility equilibria are determining elemental concentrations. For lanthanum, cerium, and thorium, the solubility of the phosphate appears to govern their concentrations in sea- water, keeping them at a remarkably low level (Table 3). Their removal from seawater, or their transfer from surface to deeper waters or to the sediments, may be enhanced by the biological cycles in which phosphate is regenerated by the decomposition of organic detritus descending through the water column. COASTAL OCEAN Several characteristics of the coastal ocean appear to be especially significant in determining the behavior of ele- ments. They are (a) rapid mixing of substances injected into the ocean; (b) circulation patterns that tend to favor retention near the coast of substances introduced into the coastal ocean; (c) relatively intense biological activity; and (d) the abundance of particles (both biogenous and litho- genous) suspended in the water. The discharge of a river quickly mixes with a volume of seawater several times as large to form a low-salinity surface layer that flows into the coastal ocean, mixing continuously. Such discharges can be identified on the basis of salinity and other parameters. The distribution of dissolved sub- stances discharged by rivers usually replicates the patterns shown by these identifying parameters. Most soluble sub- stances introduced along the shore will be mixed fairly rap- idly, even when not clearly associated with a major river discharge. The circulation of the coastal ocean tends to favor the retention of dissolved substances near the coast. The thin plume of low-salinity water formed by the discharge of a river moves along the coastline for many kilometers, carry- ing with it many of the substances injected into it. The sub-

142 Radioactivity in the Marine Environment COASTAL OCEAN OPEN OCEAN Woste D*scharges water movements part1C1e movements FIGURE 1 Schematization of the coastal and open ocean. surface circulation also tends to favor, near the coast, the retention of most substances injected into the coastal ocean. Where precipitation and runoff exceed evaporation, an estuarine-like circulation results (see Chapter 2) in which fresh water added to the ocean surface mixes with salt water from below and moves generally seaward (Figure 1). A shore- ward subsurface flow replaces the salt water that has moved upward into the surface layers. In areas where evaporation predominates, the coastal ocean does not exhibit estuarine- like circulation, but such areas are relatively uncommon. The increased nutrient supply due to this vertical circula- tion and the nutrients supplied by rivers are major causes of the relatively large primary production in the coastal ocean, because subsurface waters brought into the surface layers supply nutrients to the photic zone. Certain substances in the surface waters become asso- ciated with the descending organic debris. Chemical species released by the decomposition of particles sinking out of the surface layer will tend to be moved landward in the sub- surface flow, to return eventually to the surface layer. Al- though materials are lost to the sediments or to the surface layers of the open ocean, the circulation of the surface and subsurface waters tends to retain some chemical species in the coastal ocean. Dissolved oxygen in the near-bottom waters or in the sediment may be depleted or even completely exhausted, depending on the supply rate of dissolved oxygen relative to the rate of consumption in the decomposition of organic matter formed in the photic zone. Where exhaustion of dis- solved oxygen occurs, sulfate-reducing bacteria are involved in the production of H2S. Complete exhaustion of the dis- solved oxygen in the water column is not common in the coastal ocean except where water circulation is greatly re- stricted, as in certain fjords, or where primary productivity is extremely high. In areas of large primary productivity, where the supply rate of dissolved oxygen is large enough to prevent oxygen depletion in the near-bottom waters, H2S may nevertheless form in the sediments because the rate of oxygen diffusion into the sediment is slow. The presence of hydrogen sulfide may act as a control on the concentration of many metallic ions in seawater, as can be seen in Table 3. A sulfide ion activity of 10~9 moles/ liter, corresponding to that of a "stinking mud," results in an environment favorable to the removal of metals that form highly insoluble sulfides. Certain metals will be de- pleted even in moderately sulfide-rich water, i.e.,ag-2 = 10-13 moles/liter. Manganese and iron appear to be enriched in sulfide-rich waters inasmuch as the sulfides of the reduced forms of these elements are relatively soluble (Table 3). Higher con- centrations of manganous ions in the anoxic waters of the Black Sea, relative to the oxygenated surface waters, have been reported, apparently confirming the existence of this process of enrichment. Reactive elements brought into the ocean may become associated with land-derived solid materials. Such materials derived from organisms incorporate certain elements into their tissues or skeletons, often concentrating them ma. y- fold relative to their concentrations in seawater. After an organism's death, some of these elements are incorporated in the bottom sediment, along with undecomposed organic remains. Nutrient elements, such as phosphorus and nitro- gen, may be released as soluble species during decomposi- tion of the organic remains in the water. Particle-associated chemical species and reactive elements that were taken up by the organisms and not quickly re- leased by decomposition are eventually incorporated in the sediment, which is a major reservoir for such elements. OPEN OCEAN The open ocean differs significantly from the coastal ocean; thus, there appear to be major differences in elemental be- havior (Table 1). Among the significant differences between the coastal and open ocean are the general nutrient deficien- cies and relative scarcities of organisms and particles in sur- face layers of the latter. The well-developed density stratifi- cation in the open ocean inhibits large-scale vertical mixing and the upward movement of nutrients from deep waters, except at divergences or in high latitudes. Unreactive ele- ments generally pass through the coastal ocean into the open ocean. Reactive elements tend to become associated with particles or to be utilized by organisms and thus are removed from seawater in the coastal ocean. Elements with short residence times tend to accumulate in the sediment depos- ited in the coastal ocean; elements with long residence times tend to accumulate in the open ocean. Uranium, which can be reduced to a tetravalent state in coastal de- posits, is an exception—it has a long residence time in the ocean but tends to accumulate in inshore deposits. In the open ocean, some chemical species removed from the surface layers by organisms are released in adjacent deeper waters as the particles decompose before reaching the bottom. Among these are elements such as phosphorus and nitrogen, which are retained by the partially decom-