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3 Dynamics of the Circumpolar Current I. PRINCIPAL RECOMMENDATIONS 1. We recommend the initiation of planning for a measurement pro- gram, emphasizing presently available techniques, to study the large-scale, transient dynamics of the Antarctic Circumpolar Current (ACC) and its role in the general ocean circulation. The program can be divided into two parts: a set of specific experiments designed to explore features, heat balances, and energy sources and a continuing effort to monitor the important vector and scalar fields in the regions of the current. The elements of such a program would include the following: (a) Direct measurements with moored instruments, e.g., current meters, capable of long-term (at least one year) records; (b) The use of continuous vertical profiling instruments and bottom-mounted instruments capable of measuring average properties of the flow (pressure gauges, electromagnetic field recorders, and acoustic sounders); and (c) Lagrangian studies with drogues and middepth floats to determine the path and, together with surface measurements, to establish unambiguous tracers for the ACC. A pilot experiment is recommended, to be carried out in collaboration with FGGE planning. 2. We recommend a feasibility study on the measurement of absolute dynamic topography on an east-west section from the South Sandwich Trench to the western end of the Drake Passage. 3. We recommend that the development of remote-sensing tech- niques, e.g., satellite measurements, and instrument deployment by aircraft be strongly encouraged. 4. We recommend the encouragement of realistic theoretical and laboratory models of joint theoretical-observational experiments on the Antarctic Circumpolar Current. 12
Dynamics of the Circumpolar Current 13 II. INTRODUCTION Although it is the major current system of the world, the ACC is one of the least known. It appears to be broader (sometimes showing a biaxial nature) and is longer than any other temperate current; its transport is primarily zonal. The vertical shear is less than in other currents, and there appear to be both strong barotropic and baroclinic contributions to the trans- port. It is closely associated with the Polar Front Zone, yet the actual dynamical interaction is not understood. The associated meridional (cross- stream) fluxes may play a crucial role in determining the budgets of heat, salt, and dissolved oxygen in the world ocean. The immediate scientific goal is to establish the space and time scales for a kinematic description of the flow as a base for dynamical studies. The ultimate scientific goal is to understand the dynamical role of this region in the general oceanic and atmospheric circulation. Achievement of the first goal is still remote; even the dynamics of such well-studied currents as the Gulf Stream are elusive. The final practical goal will be the establishment of a monitoring network in the current as part of a global environmental predic- tion program. III. BRIEF HISTORY The early results, primarily based on hydrographic data [Sverdrup et al., 1942], suggest that the current is broad, has a transport equal to that of other major currents (at least 100 x 106 m3/s), and extends to the bottom, where it is deflected by at least five different ridge systems as it flows around the Antarctic continent. A chart of sea-surface topography prepared from available historical data by Gordon and Bye [1972] is shown in Figure 3.1. The width and intensity of this averaged current was found to vary greatly; constrictions occur south of New Zealand, at the Drake Passage, and near 145° W; the flow is relatively diffuse over the southeast and southwest Pacific basins. Wavelike patterns suggestive of the nonlinear, time-dependent dynamics seen in other currents at temperate latitudes appear to the lee of New Zealand and at 145° W. (From other data, an apparent strong interaction with the bottom was observed by Gordon [1971, 1972] near the Macquarie Ridge, where a large loop is formed by the current.) The variations in the sea-surface slope across the Drake Passage were found to be nearly the same as the maximum variation of 38 cm observed by McKee [1971] using monthly mean-sea-level records at the opposing coastlines (Punta Arenas and the Argentine Islands).
14 Southern Ocean Dynamics FIGURE 3.1 Sea-surface dynamic-height anomaly relative to the 2500-dbar level. The depths less than 3000 m are stippled. There are approximately 1000 data points from which the dynamic height isobaths are constructed. These data are spread smoothly over the entire region shown and have denser spacing in the Drake Passage- Scotia Sea region and lesser density between 170° W and 170° E north of 60° S. The few data points available east of the Campbell Plateau are shown to indicate the marginal control of the dynamic isobaths in that vicinity. [A. L. Gordon and J. A. T. Bye, J. Ceophys. Res. 77, 5994, 1972. Copyright by American Geophysical Union.] We note that a 38-cm difference would drive a barotropic current of transport 20 x 106 m3/s here. Thus, long-term transport changes of almost a factor of 2 are suggested. A number of recent attempts to measure the transport have combined direct current measurements with hydrography. Reid and Nowlin [1971] found from a section across the Drake Passage that the relative pressure field was consistent with earlier measurements of the Soviet research ship Ob and British RRS Discovery and concluded that when the data are treated in the same way, three various sets of historical data (two from the Discovery, one from the Ob) and their own show remarkably similar results: a geostrophic transport relative to the bottom varying from 90 to 110 x 106 m3/s. They found a transport relative to the greatest depths sampled to be 110 x 106 m3/s. Their absolute transport, based on bottom-current-meter records of 24 to 125 hours' duration was greater: 240 x 106 m3/s. One year later, Callahan [1971] used hydrographic stations and bottom-current meters along a section from Australia to Antarctica (132° E). He found an absolute transport of 230 x 106 m3/s, based on current-meter records of 25 to 50 h. In addition, Callahan's hydrography revealed narrow horizontal scales in the relative current: at 51° S the eastward flow was divided by a narrow slow counter- current to the west, over the Indian-Antarctic Ridge. This feature also ap- peared at 115 E and 140 E. Figure 3.2 shows his 132 E section.
Dynamics of the Circumpolar Current 15 A remarkable result was obtained by Foster [1972] from hy- drography and four vertical arrays of current meters across the Drake Passage in February 1970. In agreement with previous results, he found a net east- ward geostrophic transport of 72 x 106 m3/s relative to the 3000-dbar level. However, a relative transport estimate based on variable reference level yielded a value of 5 x 106 m3/s to the west, and the absolute transport obtained from the overall current-meter mean (10 days) was 15 x 106 m3/s to the west. Although near-zero transports have been inferred by Ostapoff [1960, 1961] by the variable-reference-level technique, this is the first estimate based on direct measurements of a significant westerly transport through the Drake Passage. On the basis of these observations, it is clear that the fundamental vorticity balance of the current involves contributions from several terms: wind stress, bottom topography, curvature, and time dependence. A number of theoretical studies, both analytical and numerical, have been made on the dynamics of the current and its interaction with the general abyssal circulation. Sverdrup et al. [1942] noted that the current was FIGURE 3.2 Zonal component of absolute velocity (in centimeters/second, positive east) at 132° E. Vertical exaggeration is 500 [J. E. Callahan, J. Geophys. Res. 76, 5860, 1971. Copyright by American Geophysical Union.]
16 Southern Ocean Dynamics deflected by the bottom ridge systems in a direction consistent with Ekman theory and inferred that the current must penetrate to the bottom. They also suggested that lateral friction balanced the wind stress. After the qualitative success of linear (3-plane analysis in explaining the major features of tropical and midlatitude ocean circulation, Munk and Palmen [1951] inquired into the vorticity balance of the ACC. They dis- covered that the eastward current that would be produced by the observed surface wind stress is much stronger than observed, unless an unrealistically high value is assigned to frictional dissipation. They suggested that the re- tarding pressure of submarine ridges balances the stress exerted by the surface wind and that the easterly relative flow is caused by deep water in the Antarctic Ocean drifting toward the axis of the rotating earth. Later, Stommel [1951] suggested that since nowhere in the Antarctic Ocean is there a continuous latitude with a depth greater than 1000 m, zonal theories of the current must be modified to take account of possible zonal pressure gradients. He assumed that all dissipation takes place in the Drake Passage region and found that the ACC could be qualitatively explained as a wind- driven current regime. Kamenkovich [1962] and Schulman [1970] also demonstrated the strong effects of topography, and Devine [1972] showed the importance of baroclinicity to the path of the current in the Drake Passage. Gill [1968], following the work of Stommel, pointed out the pos- sible importance of northward (turbulent) momentum flux in the vorticity balance. The numerical model of Gill and Bryan [1971], a circulation driven by imposed wind stress and temperature distributions, showed the interesting result that the force due to pressure difference across the bottom topography of a model Drake Passage was in the same direction as the wind force and was larger. Observations show that the water on the Atlantic side of the Drake Passage is colder than that on the Pacific side; thus, this "driving" pressure gradient may be real. A knowledge of absolute dynamic topography on an east-west section from the South Sandwich Trench to the western end of the Drake Passage would be required for a calculation of this difference in the real ocean. The ACC can be regarded as a baroclinic zonal jet and as such might be expected to show baroclinic waves, which could result in large meanders. However, Bowen and Stommel [1971] found from RRS Discovery stations between April 1938 and March 1939 that the position of the isotherms was notably steady. The deep flow in the region of 0 to 20° E did not move more than 160 km and perhaps moved much less. Thus, wave disturbances such as one might expect to find in a major zonal baroclinic current apparently do not exist, at least not in the relative flow.
Dynamics of the Circumpolar Current 17 The ACC interacts with other phenomena in the region. Crease [1964] has pointed out that existing ACC theories are too simple, i.e., the proper description of the dynamics of the flow must contain a description of the Antarctic Convergence. Sverdrup et al. [1942] noted that the isobaric surfaces change slope abruptly at the Convergence. Gordon [1968] has pointed out that the westward flow produced by water discharge around the continent (a mechanism proposed by Barcilon [1966]) may result in summer speed-up of the east wind drift, interior to the ACC. Conclusive evidence is not yet available. One study has deduced the transport of the ACC with a global model utilizing advection and diffusion in an idealized World Ocean Basin. The study reports a wide variation in ACC transport as a function of longitude, a conclusion that could be tested. Most recently, Thompson [1971] noted that propagating Rossby waves carrying momentum up-gradient into the weak current will cause baroclinic currents to be sharper where deeper water lies on the left, and he has used this fact to explain qualitatively Callahan's observations that the ACC is sharpest on the steeper slope of the Indian-Antarctic Ridge. Thompson suggests that concentrated currents might also be found at the northern end of the Albatross Cordillera (170° W to 140° W at 60° S) and also at the northern tlank of the Atlantic-Indian Ridge near 50° S from 5° W to 30° E. In summary, the overall vorticity balance of the current is complex, involving contributions from several forms. Estimates of total transport vary widely, although according to Gordon [1967] relative geostrophic transports seem to vary little in the Drake Passage where repeated observations have been made. Wind-driven theories of transport yield plausible values. Linear theory, as in the case of other ocean currents, reveals some of the main qualitative features but does not adequately account for time-dependence and effects of bottom topography. Nonlinear effects, including curvature and the coupling of wind and thermal driving, have not been adequately investigated. The interaction between the current and other observed features, e.g., the Polar Front, is still not clear; and the role of the region in the global oceanic and atmospheric circulation is yet to be determined. IV. RECOMMENDED PROGRAM We recommend the initiation of planning for a measurement program, emphasizing presently available techniques, to study the kinematics and dynamics of this region. The program can be divided into two parts: a pro- gram of specific experiments designed to explore features, test balances, and
18 Southern Ocean Dynamics energy sources and a continuous effort to monitor the important vector and scalar fields in the regions of the current. The first step is to establish firmly the time and space scales of the motion and the driving fluxes. Although we have a rudimentary idea of the spatial structure of the current in some regions, its time-dependence is practi- cally unknown. The dynamics may be distinctly different within different regions and time periods. Therefore, monitoring programs and special experi- ments must be designed to cover this diversity of dynamic characteristics. For example, the dynamical effect of bottom topography is complex, and the driving fluxes vary strongly with season. Experiments must be designed to yield accurate estimates of the various terms in the conservation equations if adequate theoretical models are to be devised. A series of recommendations for the elements of a possible set of dynamics experiments is presented below. These recommendations involve techniques that are being increasingly applied to other parts of the world ocean. If we are to extend our knowledge of antarctic oceanography, we must apply these techniques in the Southern Ocean now. A. ELEMENTS OF A LONG-TERM MONITORING PROGRAM 1. Flow Tracking and Surface Indicators The technology exists for the satellite tracking of surface and subsur- face drogues. Such measurements have been of particular importance in local vorticity studies in the Gulf Stream and the Kuroshio Current. The flow patterns thus measured in conjunction with other properties of the current can reveal the relative importance of the bottom topography, time- dependence, curvature, and planetary-vorticity terms in the vorticity-conser- vation equation. Deep drogues will be important in these studies, as will bottom-moored current-meter arrays. However, the Lagrangian studies them- selves are important because they give a picture of the near-surface flow, which is unobtainable any other way. Moreover, they could provide useful atmospheric and sea-surface data for meteorology, e.g., the FGGE. If such surface-drifting buoys can be made to withstand the severe seas and winds of the region, they could be used for such tracking in the ACC. One of the outgrowths of these studies should be the establishment of surface indicators for the current. For the Gulf Stream, the position of the 15 °C isotherm at 200 m has proved a reliable indicator for tracking meanders and eddies. The indicator for the ACC could be a sharp surface-temperature gradient, the position of the 1 °C isotherm at 2000 m, a visible change in surface chemistry, or some other feature. We note that Lagrangian studies
Dynamics of the Circumpolar Current 19 with drogues and middepth floats could be used to determine the path and, together with surface measurements, to establish unambiguous tracers for the ACC and recommend that a pilot experiment be attempted when the tech- nology is adequate. Such an experiment should be carried out in collabora- tion with FGGE planning. 2. Cross Sections, Profiles, and Time Series We have pointed out that the data on relative geostrophic transport through the Drake Passage are remarkably similar (or can be made to be so by using consistent reference levels) but that the data do not agree when referred to available direct current-meter measurements. One step is clear: more closely spaced and longer time series of current meter and other direct mea- surements of current profiles are needed. Moreover, each of the geographical regions that have different dynamics must be studied. We recommend that direct measurements of current and temperature initially be made in the current with moored arrays of a few instruments capable of at least four-month and preferably one-year records. The choice between a linear and a two-dimensional array is to be determined by ex- perience with moored arrays in other strong currents, e.g., the Gulf Stream. Later, more elaborate arrays could be supplemented by continuous vertical profiling instruments and bottom-mounted instruments (e.g., pressure gauges, electromagnetic-field recorders, and acoustic sounders capable of monitoring average properties of the flow). Four distinct dynamic areas suggested for study are listed, and a schematic diagram of possible instrument deployment (for the Drake Passage) is shown in Figure 3.3. This general arrangement could be used in any of the regions discussed below. For logistic ease, the first of each of these studies should be carried out, or begun and finished, during austral summers. To keep the experimental activity within reasonable bounds, the different regions should be attempted in sequence. Drake Passage-A Constraining Narrows To extend the time series of previous records, first consideration should be given to long-term measure- ments with a few instruments. Later, a more elaborate array including five strings of current meters might be distributed as pictured in Figure 3.3 with one at the convergence near the most rapid flow. Bottom-current meters should be placed close to South America in order not to miss any deep flow. Bottom-pressure gauges up either side of the passage as pictured would allow the measurement of the time-dependent behavior of several isobars and thus permit a vertical resolution of the directly measured pressure field. Mat Basin "Flat" here means that topographic effects on local vor- ticity are minimized. A possible region is the Southeast Pacific Basin, along
20 Southern Ocean Dynamics 64 °S Drake Passage CURRENT METERS PRESSURE GAUGES FIGURE 3.3 Recommended eventual arrangement of instruments across the Drake Passage; the first long-term moorings would involve fewer instruments. 100° W. A cross section of velocity profiles would be required before the moorings are set out in order to determine the spatial separation of the moorings. The density field should be monitored as often as possible across the section. East-West Ridge (e.g., Indian-Antarctic Ridge at 132° E) Here the bottom is parallel to the flow, and the vorticity balance probably is different. Indeed, the measurements of Callahan [1971] show a westerly counter- current along the ridge, and the work of Thompson [1971] emphasizes the importance of time-dependent flow there. North-South Ridge (e.g., the Macquarie Ridge of the Campbell Plateau at 140° W) In this region, the current crosses a north-south ridge and then appears to undergo a series of meanders. The flow path exhibits meanders that are superficially similar to those observed in the Gulf Stream or Kuroshio and would best be studied by the combination of techniques used in those areas. Accurate studies of meanders and local vorticity balance require both bottom current-meter arrays and path tracking by ship or airplane. To monitor the transport adequately, a two-dimensional array of moorings would be required.
Dynamics of the Circumpolar Current 21 B. A SPECIFIC EXPERIMENT The determination of the magnitude and sign of the downstream pressure gradient across any of the many ridges that the current passes over would be an important step in determining the role of these submarine ridges in either driving or opposing the ACC. In view of its importance in resolving the question of pressure gradients across the submarine ridges in the ACC, we recommend a feasibility study on the measurement of absolute dynamic topography on an east-west section from the South Sandwich Trench to the western end of Drake Passage. C. THE POLAR FRONT AND THE ANTARCTIC Cl RCUMPOLAR CURRENT The relation of the ACC and surface-temperature gradients as tracers was discussed briefly earlier. The relation of the ACC to the Polar Front Zone is a more difficult problem to solve. This zone, where a fluid mass with polar characteristics abuts one with subpolar properties, is variable and complex. Some data in this area show a convergence process, some a diver- gence. Still other data show so complicated a structure that no simple circu- lation model is obvious. The mechanism responsible for the formation of the zone and its interaction with the ACC and other dynamical processes in the Antarctic Ocean are not understood. An adequate study of the zone and its interaction with the ACC would require a detailed plan. We recommend that such a plan be developed utilizing the data available from other experiments and then carried out, if logistically feasible. The ACC affects the general oceanic circulation through the flow of mass and momentum into or from the antarctic region. This cross-stream transport is basic to our understanding of the larger role of the ACC. We note that, wherever possible, data sections along east-west lines should be en- couraged. Knowledge of cross-stream momentum flux could shed some light on the vorticity balance. For example, Gill [1968] has pointed out that an alternative to lateral friction in the vorticity balance is a northward momen- tum flux. To obtain a balance, mean values of the flux puv of about 100 dyne/cm2 are required. Assuming that the principal part of uv is due to the fluctuations of u and v about their mean values, the magnitude of the fluctu- ations would need to be at least 10 cm/s, that is, of the same order as the mean velocity. A time series of current-meter records from an array is one way of (crudely) estimating this momentum flux.
22 Southern Ocean Dynamics 3. We recommend the development of realistic theoretical and laboratory models of Antarctic Bottom Water formation. Eddy transports can be found in principle by monitoring temperature and salinity simultaneously with velocity and then estimating the divergence of the fluxes v T and v S . The present techniques are not accurate enough for this measurement. As the techniques improve, they should be attempted in sections in the current. D. DEVELOPMENT OF NEW TECHNOLOGY The Working Group notes that in most instances it will not be neces- sary to develop new technology, i.e., sensors and data-acquisition systems and their associated moorings for the Antarctic. Aside from the straightforward extension of sensor ranges and necessary strengthening against ice and heavy weather, the development of sensors carried on in other oceans by other programs appears to be adequate. TABLE 3.1 RECOMMENDED PROGRAM STRUCTURE Dynamics of the Circumpolar Current Experiments and Goals Proposed Experiments and Theory Monitoring Experiments * Long-term Eulerlan variability from moored current and temp- erature measurements * Transport variability in Drake Passage from Integrating techniques * Surface flow paths from drifting buoys * Surface temperature and properties from remote sensing Technique Development * Aircraft deployment of deep Understand space-time variability for determination of eddy fluxes of energy, heat and momentum. Use unique geography of enclosed flow to establish response and Index to large-scale atmospheric forcing of ocean currents. Synoptic view for direct gross estimates of energy budgets. Substantial reduction of logistics coats for long-term measurements. * Review of existing theory against background of survey data * Application of non-linear time-dependent jet dynamics to ACC * Laboratory models of specific ACC dynamical processes Feedback to experimental design. Rationalize existing and incoming data with basic conservation laws. Assist analytical and numerical models in detailed study of specific processes.
Dynamics of the Circumpolar Current 23 However, it is important to encourage the development of technology that promises to reduce logistics costs. A maximum use of satellite data would be a good example of time saving. The deployment of instrumentation by aircraft rather than ships also promises to be highly cost-effective. There- fore, we recommend that the development of remote sensing techniques, e.g., satellite measurements, and instrument deployment by aircraft be strongly encouraged. E. REALISTIC THEORETICAL MODELS The success of local vorticity studies on western boundary currents and the similarity of ACC paths to Gulf Stream and Kuroshio paths suggests that a similar approach could be applied with success to the ACC. We recom- mend the encouragement of construction of realistic theoretical and labora- tory models of the ACC and joint theoretical-observational experiments on the ACC. F. SUMMARY OF RECOMMENDED PROGRAM Tables 3.1 and 3.2 summarize the experiments and goals and show how the recommended program would fit into a ten-year time scale. TABLE 3.2 | RECOMMENDED PROGRAM STRUCTURE | Dynamics of the Ctrcunpolar Current Time-Phased Diagram Activity 1973 - 1976 1976 - 1S79 1979 - 1982 l^^^ CONTINUAL PLANNING AND REVIEW | 1 Monitoring Experiments â¢Surface and near-surface [Drifting Buoys 1 Moored instruments Begin planning and use â - A cooperat ive FCGE pxpt- r troont I Point measurements 1 Integrating technique. Begin usi- » place for FGCE *,] collaboration 1 KriiKKe Technology v\ Satellite Data Aircraft Data collection Instrument Deployment Begin use I Merge Into International Hi mate Research Effort ^y Apply non-linear, time- dependent jet dynanics to ACC Laboratory models of Begin planning use* / and text ing use*"^ specific ACC dynamical processes Begin interaction with experimental i ⢠\ continuing planning activity
24 Southern Ocean Dynamics REFERENCES Barcilon, V. 1966. On the influence of the peripheral Antarctic water discharge on the dynamics of the circumpolar current. J. Marine Res. 24, 269-275. (See also J. Marine Res. 25, 1-9, 1967.) Bowen, J. L., and H. Stommel. 1971. How variable is the Antarctic Circumpolar Cur- rent?, pp. 645-650 in Research in the Antarctic, L. O. Quam, ed. American Association for the Advancement of Science, Washington, D.C. Callahan, J. E. 1971. Velocity structure and flux of the Antarctic Circumpolar Current south of Australia. J. Geophys. Res. 76, 5859-5864. Crease, J. 1964. The Antarctic Circumpolar Current and convergence. Proc. Roy. Soc. (London) A281, 14-20. Devine, M. 1972. Some aspects of the dynamics of the Antarctic Circumpolar Current. J. Geophys. Res. 77, 5987-5992. Foster, L. A. 1972. Current measurements in the Drake Passage. MSc Thesis, Department of Oceanography, Dalhousie University. Gill, A. E. 1968. A linear model of the Antarctic Circumpolar Current. /. Fluid Mech. 32, 465-488. Gill, A. E., and K. Bryan. 1971. Effects of geometry on the circulation of a three- dimensional southern-hemisphere ocean model. Deep-Sea Res. 18, 685-721. Gordon, A. L. 1972. On the interaction of the Antarctic Circumpolar Current and the 1732-1734. Gordon, A. L. 1968. Comment on the peripheral Antarctic water discharge. J. Marine Res. 26, 78-79. Gordon, A. L. 1971. Antarctic polar front zone, pp. 205-221 in Antarctic Oceanology I, J. L. Reid, ed. Antarctic Res. Ser. Vol. 15. American Geophysical Union, Wash- ington, D.C. Gordon, A. L. 1972. On the interaction of the Antarctic Circumpolar Current and the Macquarie Ridge, pp. 71-78 in Antarctic Oceanology //: The Australian-New Zealand Sector, D. E. Hayes, ed. Antarctic Res. Ser. Vol. 19. American Geophys- ical Union, Washington, D.C. Gordon, A. L., and J. A. T. Bye. 1972. Surface dynamic topography of Antarctic waters. J. Geophys. Res. 77, 5993-5999. Kamenkovich, V. M. 1962. Trudy Inst. Okeanol. 56, 241-293. McKee, W. D. 1971. A note on the sea level oscillation in the neighborhood of the Drake Passage. Deep-Sea Res. 18, 547-549. Munk, W. H., and E. Palmen. 1951. Note on the dynamics of the Antarctic Circumpolar Current. Tellus 3, 53-56. Ostapoff, F. 1960. On the mass transport through the Drake Passage. J. Geophys. Res. 65, 2861-2868. Ostapoff, F. 1961. A contribution to the problem of the Drake Passage circulation. Deep-Sea Res. 8, 111-120. Reid, J. L., and W. D. Nowlin, Jr. 1971. Transport of water through the Drake Passage. Deep-Sea Res. 18, 51-64. Schulman, E. E. 1970. The Antarctic Circumpolar Current. In Proceedings of the Summer Computer Simulation Conference at NCAR, June 1970, Denver, Colo. Stommel, H. 1951. A survey of ocean current theory. Deep-Sea Res. 4, 149-184. (See also J. Marine Res. 20, 92-96, 1962.) Sverdrup, H. V., H. W. Johnson, and R. H. Fleming. 1942. The Oceans. Prentice-Hall, Englewood Cliffs, N.J., pp. 605-624. Thompson, R. O. R. Y. 1971. Structure of the Antarctic Circumpolar Current. J. Geophys. Res. 76, 8694.
