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TIDAL HYDRAULICS* F. A. Herrmann, Jr. Introduction The branch of knowledge applicable to studies of the physical aspects of tidal waterways has become known as Tidal hydraulics. n There is reason to regret the adoption of the term to include all tidal waterway engineering, as many are prone to con side r its scope to be limited to the rise and fall of the water surface in consonance with the movements of heavenly bodies that generate the forces, and to the currents that are caused by the alternately rising and falling tide. It is emphasized that the term Tidal hydraulics" has come to be understood as including, in addition to the purely hydrodynamic considerations of such tidal waterways as inlets, estuaries, maritime straits, and canals, the following: channel dimensions and alignment; shoaling, including consideration of sources of the sediment, manner of transport, and cause of deposition; training works and dredging procedure (but not dredge design); jetty and breakwater layout; the salinity of the water, including associated phenomena; and the dispersal and flushing of pollutants. This paper, however, will concentrate primarily on salinity conditions. Tidal phenomena occuring in any waterway seldom result from a single cause, but are more or less complex interactions of a number of factors. Tbus, if a change in the regimen of a waterway is desired in order to effect an improvement, the change in each contributing factor and in the resulting interaction must be determined. The principal factors to be taken into consideration are: tides, tidal currents, freshwater disabarge, salinity intrusion, volume of sediment, characteristics of beds and banks, wave action, littoral processes, and dispersal and flushing of pollutants. *Much of the information presented in this paper was developed under the Civil Works Program of the U.S. Army Corps of Engineers. Permission granted by the Chief of Engineers to publish this information is appreciated. 115

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116 Tides Tides are usually categorized as semidiurnal, mixed, or diurnal. Semidiurnal tides {Figure 1) are typical on the East Coast of the United States, and they exhibit two nearly equal tides (i.e., two nearly equal high waters and two nearly equal low waters) per lunar day (24 hr 50 min.). Mixed tides (Figure 2) common to the West Coast exhibit two markedly different tides per lunar day. Along the Gulf Coast, one of the tides per day often vanishes, resulting in a diurnal tide {Figure 3~. These tides generate an undulation in tidal waterways, and once started, it propagates upstream to some point where further progress is terminated by a barrier, or where the accumulating attrition causes the undulation to disappear. If the length of the estuary exceeds the length of the tide wave, as in the case of the Amazon River in South America, the system may contain two or more tides at the same time. Thus, the tide may be rising or falling in two or more reaches of the estuary at the same time. In some situations, the geometry of the waterway causes a stationary wave, but these cases are not so frequently encountered as the so-called progressive waves. Progressive waves travel upstream with a celerity related to water depth. Thus, during the propagation of a progressive wave, the high-water portions travel faster than the low-water portions of the wave, and this helps to distort the shape of the wave. As the wave progresses up the estuary, the duration of the rice decreases and the rate of rise increase=; conversely, the duration of fall increases and the rate of fall decreases. The shape of a curve representing tidal heights plotted against time shifts from that approximating a sine or cosine curve to that exhibiting a quick rise of relatively abort duration followed by a slow fall of relatively long duration. Tidal conditions within a waterway depend basically on the exciting tide, the shape of the waterway, and tbe bottom friction. In a converging waterway, where friction is a secondary factor, tidal amplitude increases as the tidal wave progresses upstream. In diverging waterways, or those in which friction is more important than shape, tidal amplitude decreases as the wave progresses upstream. In addition, reflections can either increase or decrease the amplitude. Figure 4 ~how. the relative tidal amplitude along the Delaware estuary. Rapid convergence in the bay causes an increase in amplitude in the downstream area. In the next reach, the amplitude decreases, apparently from reflections from two large island=. In the upper reaches, convergence again causes the tidal amplitude to increase. Tidal range varies greatly throughout the U.S. The tide range in Gulf Coast estuaries is generally less than 2.0 feet, while tide ranges greater than 30 feet are common in Cook Inlet, Alaska. Tidal Currents As the tide wave progresses through a waterway, tidal currents are generated. Although a flood current basically occurs with a rising

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117 0~ 2 _ ~ . ~O . 1 1 1 _ D 2 4 6 12r 10 8 . 6 C: 4 S 2 -2 CHARLESTON HARBOR i1 1\ ~ 8 10 17 14 36 18 20 ~24 0 TIME, HR TYPICAL SEMIDIURNAL TIDE (1) GRAYS HARBOR, WA ~\ /: _ 1 1 1 1 1 1 1 1 ~I I I 0 2 4 6 8 10 12 14 16 t8 20 22 240 TIME, HR TYPICAL MIXED TIDE (2) Figures 1 and 2. Typical semidiurnal tide of East Coast (1), and typical mixed tide of West Coast (2~. ATCHAFALAYA BAY, LA 2.0 O~ 1.5 =~ 1.0 ~ - 0.5 ~ o Sr c, 3 1.0 Ul ~ ~ C C~ 0.5 O AUG 1976 TIME, DAYS 1 1 1 1 1 1 1 1 1 1- 1 1 ~1 1 1 1 1 1 1 8 24 6 12 18 AUG 18, 1976 AUG 19,1976 TIME. HR TYPICAL DIURNAL TIDE Figure 3. Typical diurnal tide of Gulf Coast. _ _ _ f ! t! ll t! ~ ~ I ~ ~ ~ ~ ~ ~ ~ ~ ~ I I I I I I I I I I I I 1 1 ~ I 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 1 2 | SEPTEMBER t976

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118 TRENTON 0.8 0.6 04r 1 1 O 2 - OCEAN 1.0 1 i ' - I. ll '~ ~ ~ ~q i _ 4 6 8 D I STANCE,, FT X I O DELAWARE ESTUARY Figure 4. Tidal amplitude increases with con- vergence in Delaware Bay; decreases with reflection. 3 8 J ~ 6 z o ,- 4 J 2 C] F o 14 CURR~/T~' _ _ _ . , ~ - _ . . , . . . ~ . , , , ~ ~/DE 1 2 3 4 5 6 7 8 9 10 1 1 12 TIME, HOURS DELAWARE BAY Fig~re 5. Typical tide-velocity relation. 20,000 ~o,~ B. ~ 1,~ z 500 z ~r .o 100 50 0 o 50 C} 2 J ~ ~' O ~ o to J 2lD ~ I,,,, > 4 - /~? 5 . jz ~ S S - 1 1 100 lISO 200 260 300 350 1,000~fT CHANNEL STATIONS FROI~ f~llLADELPHIA EFFECTS Of FRESH~WATER DISCHARGE figure 6. ON eOTTOM SALINI" AT HIG^WATER S~K ~E" ~DE

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119 tide, there is generally a significant phase difference between the current and tide. The current flow will generally be in the ~wrong. direction for an hour or two after the tide has changed. A typical tide-velocity relation is shown in Figure 5. Although low tide occurs at he 4.0 in this example, the current continues to ebb until hr 5.5. Similarly, high water occurs at hr 10.0, but tbe corresponding slack current Is delayed until hr 11.5. In general, the tidal currents in the lower portions of a tidal waterway will greatly exceed the magnitude of freshwater currents resulting from upland discharges. Freshwater Discharge The freshwater discharges into the tidal waterway have profound effects on the regimen. They affect the basic tide independently of the effects of geometry, greatly modify the resultant current by lengthening the ebb and shortening the flood, transport upland sediment to the tidal waterway, and interact with salinity intrusion forces to produce density currents. Additionally, the inflow of fresh water is the means by which a tidal waterway purges itself of pollutants introduced by man, and variations in the freshwater discharge rate alter the extent of salinity intrusion, as shown for the Delaware estuary in Figure 6. Salinity Engineers are interested in salinity conditions in an estuary for several reasons. As I will explain later, salinity intrusion can have a profound effect on the direction, magnitude, and duration of currents. Salinity also plays an important role in determining the sedimentation and circulation characteristics of an estuary. Government agencies and private concerns use water from estuaries for drinking water supplies, irrigation, and industrial purposes, and they are thus concerned with the possibility of saltwater contamination of their water sources. Salinity is also vital to the ecology of an estuary. The various fish and wildlife are tolerant to salinity in varying degrees. Thus, if salinity conditions were drastically altered, certain species might be driven out of the area. For these and other reasons, it is necessary to understand the significance of existing salinity conditions and be able to predict the changes in salinity conditions that might be brought about by some man-made change in the estuary. Tidal action and freshwater discharge normally provide the primary mechanisms for mixing salt and fresh waters as a result of tidal currents. Salinity characteristics in real estuaries can be classified into three broad categories: highly stratified, partly mixed, and well mixed. In a highly stratified estuary, a distinct saltwater wedge will be present. In a well-mixed estuary, the salinity from surface to bottom will be essentially uniform. The partly mixed case falls in

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fRESW WATE~ ~. ~ ~- ~.SALT WATER . ~ 1,,,~:,;,;;,.,,,,,,,,,;,.,;,;;;,,,,,. CONDITIONS TYPICAL OF I GH LY "STRATI Fl ED ESTUARY Figure 7. FRESH WATER I SALT ~ VATER ~O =~000~2 44 FLOOD EBB FLOOD EBB TYPIGAL DISTRIBUTION OF VELOCITY IN HIGHLY STRATIFIED ESTUARY Figure 8. +'o ~ 1 ~ ~ 1 1 ~ _ ~ Z3 ~ ~5 , ~O./ _ - o72 ~ r,-~/ ~76 , ~oZ/ ~ - ~/ , - 7. 6 6.B ~6.9, -74 - - 0-65 ~06.2 ~ o7.d _ 06.2 . 4,5.3, oZ4 ~ - 05.0 ~0,fO ., .6.0 . ~5` ~`~55 o68 a ~/~ Of ~EF TIES ~ ' J 10 ~ 20 z o i_ 30 J 40 Figure 9. _ ~/ ~0 750 , _6.5 ~ 0` /- _ o6.d ~- 6.9 , - 5.9 ~3.t _o6~3- ~5.5. ,~.5- as _ ~5.8, 3.4 35 ~8ULE/JT - oS. ~/.9 // ~;___ - d#. ,G ~0/,# o,` ~.0 ~ ~ APPROX L/WE OF REKE~SE QOW - o~ _ ,~ ~ _~ /.6 , ,9 /4, SO _ ~ 1 1 1 1 1 1 1 1 1 1 1 ~-~ ~0 19.S . 20.0 20.5 21.0 MILES eELOW HEAD OF PASSES SOUTHWEST PASS VELOC ITY Dl ST R IB U T I ON FRESH-WATER DISCHARGE 300,000 CFS

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121 between the other two, having a distinct vertical salinity gradient, but not a wedge. In an ideal case of a highly stratified estuary, the freshwater velocity and the tidal currents are not great enough to create appreciable mixing of the salt and fresh waters, but the shear stress of the fresh water on the face of the saltwater wedge will cause a reversal of current direction within the saltwater wedge (Figure 7~. The salt water moves upstream at the bottom of the wedge but downstream at the top of the wedge. In addition, the wedge will move upstream and downstream in phase with the tide. The extent to which the wedge intrudes upstream depends on the freshwater discharge, the channel depth, and the density difference between the flab and sea waters. Typical velocity distributions in a highly stratified estuary are shown in Figure 8. Upstream from the limit of saltwater intrusion, the direction of the current is the same at all depth", and since there is normally no reversal of flow by tidal action in a highly stratified estuary, the current direction is downstream at all times. In the region of saline intrusion, the direction of the current from the surface to somewhat below the salt-fresb water interface i" downstream. However, that near the bottom is upstream to compensate for the salt water being lost from the interface by mixing and for the salt water flowing downstream within the wedge. Because there is virtually no mixing at the interface, the water above the interface has essentially zero salinity, while that below the interface is essentially seawater. Southwest Pass of the Mississippi River is the best example of a highly stratified estuary. Figure 9 shows the velocity distribution (averaged over a tidal cycle) at the mouth of the Pass for a river discharge of about 750,000 cubic feet per second (cfs). Flow in the Southwest Pass was 300,000 cfs. The line of zero velocity is slightly below the interface. For this discharge, the tip of the saltwater wedge is located adjacent to the outer ends of the jetties. The upstream extent of saltwater penetration is dependent on the magnitude of the freshwater discharge, as shown in Figure 10. For an extremely low river discharge, the wedge intrudes upstream about 140 miles, which is upstream from New Orleans. Whereas the highly stratified type of estuary was characterized by a two-layered system with zero salinity in the surface layer and sea salinity in the bottom layer, the well-mixed case is characterized by essentially uniform salinity from surface to bottom (Figure 11~. The salinity at the entrance to the estuary is that of seawater; and it decreases with distance upstream from the entrance. Density currents in a well-mixed system are not completely eliminated, but they are much weaker than in a stratified system or than the tidal currents. There is a complete reversal of flow direction at all depths with the changing tide. Velocity distributions typical of well-mixed estuaries are shown in Figure 12. The currents reverse with tidal phase throughout the estuary. In the fresh and brackish water regions, ebb currents at all depths predominate slightly over flood currents because of the freshwater disabarge. In the intermediate and highly saline regions, however, the bottom flood currents usually predominate slightly over

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n_ 0 ~7 I 200,000 CFS _' 300,000 CfS _p doo,ooo CfS =4 /~J , . . 1~ THALWEG l 10 t2 14 18 10 ~r . , __ ,__. i/' ~..! __ 22 ~ILES BELOW HEAD OF PASSES PROFILES OF SALT-WATER INTERFACE SOUT~ES' r~se. - ~m RIVER Figure 10. Freshwater discharge determines penetration of saltwater upstream. /////,~H/GA/ T/DE ~LOW T/DE I i!ll ,, ,~, , , ,,, ~,iY r ~ / I ~ ~ / ~ ~ r r r I / ~ '.1 ~ r r ~ r [' ~ / ~ ~ ~ I / /~7;~/ /~///////// Figure 11. Conditions typical of well- mixed estuary. FRESH WATER ~ 4 2 O 2 ___ fLOOD EBB 1~(PICAL DISTRIBUTION OF VELOGITY IN WELL MIXED ESTUARY Figure 12. rl lool- I ~- - fLOOD EBB - SALT WATER I I I , ~ .c l 20- ~ 3C J 40 i_ 23 O ~ 60 - ~x Z 4,l ~ < 8^v ~ , 1! ~ O __ 14 4.vv ~1 LO~ D/~ ~ ~SC~~G~ so 70 so 4~_D/S~RG~ ~ILE5 ~e~ ~H SALINITY F!ROFILES ~ DELAWARE RIVER Figure 13.

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123 the bottom ebb currents. Salinities decrease more or leas progressively from seawater at the entrance to fresh water in the upper reaches, and bottom salinities normally exceed those at the surface by 15 to 25 percent. The Delaware River estuary is a typical example of a well-mixed system. Surface and bottom salinity profiles are shown in Figure 13, and it can be seen that there is essentially no vertical salinity gradient anywhere along the estuary. As in the highly stratified case, the upstream extent of saltwater intrusion is dependent on the freshwater inflow, as can be seen in Figure 13. The partly mixed type is obviously an intermediate step between highly stratified and well mixed (Figure 14~. The tidal mixing forces are great enough to break up the well-defined wedge, but not strong enough to effect complete mixing. The "interface" at high tide Is considerably steeper than at low tide, and the Interface moves over a considerable distance in the estuary with each tide. As In the well-mixed case, there is a reversal of flow direction at all depths with the changing tide. When the current changes from flood to ebb, the reversal at all depths occurs almost simultaneously. However, when the current changes from ebb to flood in the lower portions of a partly mixed estuary, reversal at the bottom occurs as much as two hours before reversal at the surface. Thus, at the bottom, the duration of flood flow is usually greater than the duration of ebb flow. In the region of the estuary just upstream from saltwater intrusion, the current at all depths reverses with tidal phase, and the vertical distribution of the current in either direction is similar to that in an upland river; the downstream current at all depths predominates over the upstream current because of the freshwater discharge (Figure 151. In the region of saltwater intrusion, the direction of the current both above and below the interface reverses with tidal phase. Above the interface, the net flow is downstream; below the interface, the net flow is upstream. The interface between the fresher water in the surface strata and the saltier water underneath is not so well defined as in the highly stratified type; however, the presence of the Interface is often indicated by a discontinuity of either the vertical salinity profile or the vertical velocity profile. Savannah Harbor is an example of a partly mixed estuary. Typical salinity gradients at the entrance and about ten miles upstream are shown in Figure 16. It was previously pointed out that the length of saltwater intrusion varies with the freshwater discharge. For any of the three mixing types, it has been found that an increase in freshwater discharge reduces the length of saltwater intrusion. However, the turbulent mixing generated by the tidal currents is more important than is the freshwater discharge. The Lower Mississippi River (highly stratified) and the Delaware River (well mixed) both have controlling depths of 40 ft. In the Mississippi River, a net downstream freshwater velocity of 0.83 feet per second (fps) results In an intrusion length of 125 miles for a river discharge of 128,000 Ifs. On the other hand,

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h//Gh/ T/OE LOW t/DE~ //~/ 17,,,7 Figure 14. ~20 40 o - 60 z ~0 CL CONDITIONS TYPICAL OF PARTLY MIXED ESTUARY O FRESH WATER l _ I I l l I l I l 100 11 _ 4 2 O 2 4 4 fLOOD EBB o: SO ~, < 100 o z v SO Figure 15. \ l \ ~ HIoH ~TIDt \ ~ 20 - ENTRANCE ~o \\~/GH T/DE LOW _,>< \ 1 ~ \ I I / 1_ 1/ t _ SAL7 WAT ER O t / 1, 1. zo ~w 0 J 40 60z 80 ~ FLOOD E 68 100 TYPICAL DISTRIBUTION OF VELOCITY IN PARTLY MIXED ESTUARY c, 6 z o ~ 2 l~ n I,~ V ~ 2 : ~BB / - - 1 1 1 1 1 TOTAL AREA SUBTENDED BY BOTH EBB AND fLOOD CURVES =TOTAL fLOW 2 0m Z 2- o 4 AREA SUSTENDED BY EBB CURVE DIVIDED BY TOTAL 43 I3J AREA-PERCENT OF TOTAL FLOW DOWNSTREAM 6 1 1 1 1 1 1 6> 0 2 4 6 8 10 12 TIME IN HOURS ~FL OOD ~oo 0 20 40 SALI N ITY, P PT 10 M I L ES UPSTREAM COMPUTAT I ON OF FLOW Dl STR I BUTI O N SAVANNAH HARBOR Figure 16. Figure 1 7.

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125 in the Delaware River, a net downstream freshwater velocity of only 0.13 fps holds the intrusion length to 70 miles for a river discharge of 12,000 cfs. The Mississippi River is a very narrow estuary and has a tide range of only about 1-2 feet. It thus teas a relatively small tidal prism. The Delaware, on the other hand, has a very broad bay and a tide range of 5-6 feet. It thus has a relatively large tidal prism. Mixing It has been found that the degree of mixing is generally a function of the ratio of the freshwater discharge over a tidal cycle to the tidal prism, where tidal prism is defined as the total volume of water entering the estuary from the sea during the flood (rising) tide. When the freshwater inflow is high compared to the tidal prism (ratio greater than about 0.8), the stratified condition results. When the opposite is true (ratio less than about 0.1), the well-mixed condition results. It should be noted, however, that the degree of mixing can be affected by several other factors such as wind, waves, ships, and turbulence at the mouths of tributaries and channel constrictions. The freshwater discharge/tidal prism ratio is by no means an exact measure of the degree of mixing. It is not possible, for example, to define accurately the relative degree of mixing among estuaries having reasonably similar stratification conditions. Perhaps a more reliable parameter for defining the degree of stratification in the Estuary number n developed by Harleman and Ippen. The estuary number is defined as P F 2 estuary number = t o QfT where Pt = tidal prism (the volume of seawater entering the estuary on the flood tide) u Fo = Froude number =v~;~; uO is the maximum flood tide velocity at the ocean entrance, and h is the mean depth of the estuary Of = freshwater discharge T = tidal period The degree of stratification increases with decreasing value of the estuary number. An estuary may be changed from bighly stratified to partly mixed or well mixed by reduction of the freshwater disabarge; conversely, one may be changed from well mixed or partly mixed to partly mixed or

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126 highly stratified by increasing the freshwater discharge. Such a change can be effected by a long-term change in freshwater discharge resulting from upstream flow modification or by seasonal changes in freshwater discharge. Minor changes in mixing types are being constantly effected by deepening, widening, lengthening, or other improvements to estuary channels for navigation. As channels are dredged deeper and deeper, the salt water penetrates farther into the estuary and the degree of vertical stratification of the fresh and salt water is increased because of increased tidal prism and reduced tidal current velocities. Flow Predominance I now want to introduce the concept of flow predominance. This is a very useful concept for analyzing velocities, especially with respect to density currents. For this method, velocity observations are made at several depths at a given location, and the data are reduced to an expression which tells whether the predominant flow at each depth is upstream or downstream and in what percentage of the total flow at that point. A conventional plot of velocity vs. time is made for the observations at each point (Figure 17~. The area subtended by the ebb curve is then divided by the sum of the ebb and flood curve areas. The result defines what percentage of the total flow per tidal cycle at that point is directed downstream, and is referred to as the ebb predominance. At the bottom of a saltwater wedge, the flow predominance can be 100 percent upstream; while in the freshwater layer at the surface, it can be 100 percent downstream, as shown in Figure 18. Near the entrance of a well-mixed estuary, the flow predominance will be slightly upstream at the bottom, but more strongly downstream at the surface, as shown in Figure 18. Farther upstream, the flow predominance will be downstream throughout the entire depth. In a partly mixed estuary, upstream bottom predominance will be fairly strong at the entrance {Figure 18), and will extend a considerable distance upstream. Surface flow predominance will be strongly downstream througbout the estuary, except in areas under the influence of large-scale eddies. To obtain a broader impression of flow conditions in the estuary, it is possible to plot a profile of flow predominance along the estuary at various depths. That location along the channel at which the net flow i" balanced (50 percent ebb) is called the null point. That is, there is no net flow in either direction. The surface and bottom flow predominance for Savannah Harbor are shown in Figure 19. The null point on the bottom for this freshwater discharge is located where the dashed line crosses the 50 percent downstream line. An alternate means of determining time-average flow conditions at any point is referred to as velocity predominance. In this case, it is only necessary to determine the velocity at any point averaged over a complete tidal cycle. The result is then ~nondimensionalized~ by dividing by the freshwater velocity. An advantage of the velocity

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127 C) ~ 50 o z P~RrLY "/~a ,/1/ELL /~/J(ED- ~: H/GA/LY / sr~Ar/~/~> 1004 50 100 PERCENT OF FLOW DOWNSTREAM T YP I CAL FLOW PRE DOMINANCES Figure 18. ~ 75r ~1 1 1 1 1 1 17~ 1r z 3 o o ~50 o z = 0 - MEANTIDE ~ ~~ z _ RIVER O~5670 CfS ~_ ~_ ~ _ ~ I I ~ I I ~ ~ 25 __ 93 1 13 133 153 173 ~3 1000 Ft CHANNEL STATIONS RELATION BETWEEN NORMaL SURFAGE AND BOTTOM FLOW IN SaVANNAH HARBOR ,'A/~EL ~O~L/NG VFRY \ /~/F~VY/W TH/S~F~CH ~ _ ~, , `, _ 50 Figure 19. 4 ~ ~' ~ ~ ~ ~ r~ ~----_ _ ~ r 1 C af - 7,vCO CFS I I 3 `` n Q Qf- ,C30 CFS ~o Qf - ~8,230 CFS ~I _~ 2 ~__\\~_~ ~ ~;' O ~ DELAl2AR ~ . 1 0.01 0.05 0.1 0.5 1 l SHOALING FOR TWO-~JEEK PERIOD SOUTHWEST PASS, MISS. RIVER Figure 2 1. _1 L 1_ I I I ~ I I I I I I I I ~ I , Vf % 4(AP) BOTTOM VELOCITY CORRELATION Figure 20. \~ ~ ( ArtANr/C ~'\ ~' NF~ 1 1 ' 1 ~ ~ I SAVANNAH I 1 1 . I I I L f~LL' l ,_ LOCATION MAP SAVANNAH HAR BOR ll ~/ Figure 22.

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128 predominance method is that it appears to have a unique correlation with the local densimetric Froude number for a given estuary, as shown in Figure 20. It appears that this correlation is not affected by changes in freshwater discharge, tidal amplitude, or channel depth. Thus, it should be possible to predict the position of the bottom null point for various disabarges or depths. Salinity Effects on Shoaling Saltwater intrusion plays an important role in estuarine sedimentation. First, the salt water probably causes flocculation of suspended clays, which prevents them from being carried to sea in the upper flow layer. Second, density currents can move sediments upstream along the bottom to the vicinity of the flow predominance null point. For highly stratified estuaries, rapid shoaling will be experienced at the tip of the saltwater wedge. As mentioned before, the tip of the saltwater wedge at Southwest Pass is located at the outer end of the jetties for a discharge in the pass of about 300,000 cfs. The shoaling pattern developed in a two-week period with a freshwater discharge varying from 248,000 to 294,000 cfs is shown in Figure 21. The shoaling does indeed bracket the tip of the saltwater wedge. Note that the maximum change in depth was 28 feet. In partly mixed estuaries, the flow predominance null point usually is an area of heavy shoaling. In well-mixed estuaries, however, that is not usually the case, since density currents are quite weak. Savannah Harbor Savannah Harbor (Figure 22) is an excellent example of a partly mixed estuary. More than 75 percent of the flow is carried through Front River and North Channel. The relation between the bottom flow predominance and the shoaling rate in the navigation channel is shown quite dramatically in Figure 23. Of an annual shoaling of roughly seven million cubic yards, more than two-thirds occurs in the six-mile reach which brackets the bottom flow predominance null point. Savannah Harbor also gives a striking example of the effects of increasing channel depth on shoaling. The navigation channel has been progressively dredged from 26 feet in 1889 to its present depth of 36 and 34 feet. Profiles of the various channels are shown in Figure 24. Reliable dredging records are available for the periods indicated in the figure. For purposes of analysis, the navigation channel was divided into thirds, and the average annual shoaling rate was determined for each of the four time periods for each channel section (Figure 25~. The shoaling rate in the downstream third has decreased steadily, so that almost no dredging in now required. In the central third, the shoaling rate increased rapidly until the present channel was constructed, then it decreased significantly. The upstream third ebows a very rapid increase in shoaling. By examining these data, we can

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129 Z J oo _ - ~n~ ~ ~ O o 'z-10 0~ _O a ~Z OCR for page 115
130 follow the upstream migration of the zone of primary shoaling and, by implication, the null point of the bottom flow predominance. The upper dashed line in Figure 25 shows that the harbor-wide shoaling rate increased essentially linearly until the final and most drastic deepening was effected. In this final period, harbor-wide shoaling exhibited a much smaller increase than for the previous channel deepenings. This indicates that by the time of the final deepening, density effects in the harbor had developed to suab a degree that almost all potential shoaling material was trapped within the harbor. Thus, there was an upstream shift in the region of heaviest shoaling but relatively little increase in the total volume of annual shoaling. The early upstream migration of the major shoal area was not a significant problem because disposal areas for dredged material from earlier dredging operations were readily available. In the last time period, however, the region of major shoaling was in the port area, where disposal areas are not readily accessible. Those that are available are rapidly being filled. Thus, in addition to greatly increasing the volume of material that must be dredged, the enlarged channel shifted the location of the shoaling to an area where disposal of the dredged material is increasingly difficult and expensive. Such a change in maintenance operations and costs should be identified in the design process to enable determination of overall project costs and potential environmental problems. DISCUSSION WEBSTER: Have you investigated what forces act on the ships, or how ships maneuver when the current is going one way on the surface and another way below? HERRMANN: No, we haven't. In the reports of some investigations, we have noted areas where these types of currents seem particularly severe. We communicate the results to the field offices doing the design work. I am not sure whether they take that sort of thing into account, but it certainly could be a problem. SEARLE: Based upon a lot of experience finding and raising ship" on the bottom of the ocean, T believe current curves that are plotted over a tidal cycle are useless. You have to plot the tidal current in the vertical column across the full lunar cycle. I can cite you several examples. A salvage operation we are now engaged in, for example, in Newfoundland: at one end of the tidal cycle, you get a reversal of the current. To me, supervising divers on the bottom, reversal of the current means that I get zero current for perhaps 5 minutes or 10 minutes or 30 minutes: I get a low-current window. At other parts of the tidal cycle, the lunar cycle, there is no reversal in some places in the world. If you need to know the forces exerted by currents on a ship, you must know the tidal stage and the lunar cycle stage.

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131 BERRHANN: This has other implications. We have a model of the Cbesapeake Bay and during this past year, I guess it was, we were asked if we could help to locate some barges that had sunk. The Coast Guard was concentrating its efforts downstream from the location where they sank. With our knowledge of what the currents were in that area, we said, the predominance of flow in the bottom is upstream. Go upstream and look for them. They found them upstream. SEARLE: Yes, T can cite you cases of looking for a sunken barge. If you look for it at a particular time in the tidal cycle, you will find it. At another part of the lunar cycle, you won't find it.

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