Mixing in the Tidal Environment
Publication: Journal of Hydraulic Engineering
Volume 123, Issue 4
Abstract
A review is given of mathematical and computer modeling of many of the physical processes that effect the dilution of tracers released in tidal flows: tidal trapping, differences across the flow in tidal speeds, density currents, flow separation. The modeling approaches given most emphasis are tidal trapping, shear dispersion, chaotic stirring, and particle tracking. The central theme of this review is that during the first few tidal cycles, stretching, twisting, and splitting of the tracer patch gives rapidly increasing rates of dilution. There is a water depth (about 30 m) or estuary width (about 200 m) at which the tidal contribution to the eventual dilution rate is largest (about 3 km2 d−1 or 35 m2 s−1). Careful selection of the position, timing, and release rate of a discharge can allow a given amount of effluent to be diluted much more rapidly and to have a much reduced environmental impact.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Allen, C. M.(1982). “Numerical simulation of contaminant dispersion in estuary flows.”Proc., Royal Soc. of London, London, U.K., Series A, 381, 179–194.
2.
Aref, H. (1984). “Stirring by chaotic advection.”J. Fluid Mech., 143(June), 1–21.
3.
Arons, A. B., and Stommel, H.(1951). “A mixing length theory of tidal flushing.”Trans. Am. Geophys. Union, 32, 419–21.
4.
Awaji, T. A., Imasato, N., and Kunshi, H.(1980). “Tidal exchange through a strait: A numerical experiment using a simple model basin.”J. Phys. Oceanography, 10, 1499–1508.
5.
Beer, T., and Young, P. C.(1983). “Longitudinal dispersion in natural streams.”J. Envir. Engrg., ASCE, 109(5), 1049–1067.
6.
Beerens, S. P., Ridderinkhof, H., and Zimmerman, J. T. F.(1994). “An analytical study of chaotic stirring in tidal areas.”Chaos, Solitons and Fractals, 4(6), 1011–1029.
7.
Bikangaga, J. H., and Nassehi, V.(1995). “Application of computer modeling techniques to the determination of optimum effluent discharge policies in tidal water systems.”Water Res., 29, 2367–2375.
8.
Bowden, K. F.(1963). “The mixing processes in a tidal estuary.”Int. J. Air and Water Pollution, 7, 1–10.
9.
Bowden, K. F. (1981). “Turbulent mixing in estuaries.”Oc. Mgmt., 6(2–3), 117–135.
10.
Brown, W. S., and Arellano, E.(1980). “The application of a segmented tidal mixing model to the Great-Bay Estuary, NH.”Estuaries, 3(4), 248–257.
11.
Chatwin, P. C.(1975). “On the longitudinal dispersion of contaminants in oscillating flow in tubes.”J. Fluid Mech., 71(3), 513–527.
12.
Chatwin, P. C.(1976). “Some remarks on the maintenance of the salinity distribution in estuaries.”Estuarine and Coast. Marine Sci., 4, 555–566.
13.
Dimou, K. N., and Adams, E. E.(1993). “A random-walk, particle tracking model for well-mixed estuaries and coastal waters.”Estuarine Coast. and Shelf Sci., 37(1), 99–110.
14.
Dorrestein, R.(1960). “On the distribution of salinity and of some other properties in the water of the Ems estuary.”Verh. K. ned. geol.-mijnb. Genoot., 19, 43–74.
15.
Dronkers, J., and Zimmerman, J. T. F. (1982). “Some principles of mixing in a tidal lagoon.”Oceanology Acta, Special Vol., 107–117.
16.
Dyer, K. R. (1988). “Tidally generated estuarine mixing processes.”Hydrodynamics of estuaries, B. Kjerve, ed., CRC Press, Boca Raton, Fla., 41–57.
17.
Dyer, K. R., and Taylor, P. A.(1973). “A segmented prism model of tidal mixing.”Estuarine and Coast. Marine Sci., 1, 411–418.
18.
Fischer, H. B.(1967). “The mechanics of dispersion in natural streams.”J. Hydr. Div., ASCE, 93, 187–216.
19.
Fischer, H. B.(1972). “Mass transport mechanisms in partially stratified estuaries.”J. Fluid Mech., Cambridge, U.K., 53(4), 691–687.
20.
Fischer, H. B.(1976). “Mixing and dispersion in estuaries.”Annu. Rev. of Fluid Mech., 8, 107–133.
21.
Fischer, H. B. (1978). “On the tensor form of the bulk dispersion coefficient in a bounded skewed shear flow.”J. Geophys. Res., 83(May), 2372–2375.
22.
Fischer, H. B., Brooks, N. H., Imberger, J., Koh, R. C. Y., and List, E. J. (1979). Mixing in inland and coastal waters. Academic Press, New York, N.Y.
23.
Geyer, W. R. (1993). “3-dimensional tidal flow around headlands.”J. Geophys. Res. Oc., 98(C1), 955–966.
24.
Geyer, W. R., and Signell, R. P.(1992). “A reassessment of the role of tidal dispersion in estuaries and bays.”Estuaries, 15(2), 97–108.
25.
Giles, R. T.(1995). “Optimal strategies for discharging pollutants into narrow estuaries.”Water Res., 29(2), 563–569.
26.
Guymer, I., and West, J. R.(1988). “The determination of estuarine diffusion-coefficients using a fluorimetric dye tracing technique.”Estuarine Coast. and Shelf Sci., 27(3), 297–310.
27.
Guymer, I., and West, J. R.(1991). “Field studies of the flow structure in a straight reach of the conwy estuary.”Estuarine Coast. and Shelf Sci., 32(6), 581–596.
28.
Guymer, I., and West, J. R.(1992). “Longitudinal dispersion coefficients in estuary.”J. Hydr. Engrg., ASCE, 118(5), 718–734.
29.
Hamilton, P., Gunn, J. T., and Cannon, G. A.(1985). “A box model of Puget Sound.”Estuarine Coast. and Shelf Sci., 20(6), 673–692.
30.
Hamrick, J. M.(1986). “Long-term dispersion in unsteady skewed free surface flow.”Estuarine, Coast. and Shelf Sci., 23, 807–845.
31.
Hansen, D. V., and Rattray, M. Jr.(1965). “Gravitational circulation in straits and estuaries.”J. Marine Res., 23, 104–122.
32.
Hansen, D. V., and Rattray, M. Jr.(1966). “New dimensions in estuary classification.”Limnology and Oceanography, 9, 319–326.
33.
Heemink, A. W.(1990). “Stochastic modeling of dispersion in shallow-water.”Stochastic Hydrol. and Hydr., 4(2), 161–174.
34.
Heemink, A. W.(1993). “Tidally averaged models for dispersion in shallow-water.”Water Resour. Res., 29(3), 607–617.
35.
Holley, E. R.(1969). “Difference modeling of stream pollution.”J. Sanit. Engrg. Div., 95, 968–972.
36.
Holley, E. R., Harleman, D. R. F., and Fischer, H. B.(1970). “Dispersion in homogeneous estuary flow.”J. Hydr. Div., ASCE, 96, 1691–1709.
37.
Hunter, J. R. (1987). “The application of Lagrangian particle-tracking techniques to modeling of dispersion in the sea.”Numerical modeling: Applications to marine systems, J. Noye, ed., North-Holland, Amsterdam, The Netherlands, 257–269.
38.
Hunter, J. R., Craig, P. D., and Phillips, H. E.(1993). “On the use of random-walk models with spatially-variable diffusivity.”J. Computational Phys., 106(2), 366–376.
39.
Kay, A.(1987). “The effect of cross-stream depth variations upon contaminant dispersion in a vertically well-mixed current.”Estuarine Coast. and Shelf Sci., 24(2), 177–204.
40.
Kay, A.(1990). “Advection-diffusion in reversing and oscillating flows. 1. The effect of a single reversal.”IMA J. Appl. Math., 45(2), 115–137.
41.
Ketchum, B. (1951). “The dispersion and fate of pollution discharged into tidal waters, and the viability of enteric bacteria in the area.”WHOI Reference No. 51-11, Woods Hole Oceanographic Instn., Woods Hole, Mass.
42.
Kroll, M. S. (1990). “The method of averaging in partial differential equations,” PhD thesis, Univ. of Utrecht, The Netherlands.
43.
Kuo, A. Y., and Neilson, B. J. (1988). “A modified tidal prism model for water-quality in small coastal embayments.”Water Sci. and Technol., 20(6–7), 133–142.
44.
Li, W. H., and Kozlowski, M. E.(1974). “DO-sag in oscillating flow.”J. Envir. Engrg. Div., ASCE, 100, 837–854.
45.
Macdonald, G. J., and Weisman, R. N.(1977). “Oxygen sag in a tidal river.”J. Envir. Engrg. Div., ASCE, 103, 473–488.
46.
Malik, N. A., Perkins, R. J., and Evans, G. P. (1990). “Computational modeling of dispersion in coastal, estuarine and river regions with application to sediment transport.”Rep. for WRc, Dept. of Appl. Math. and Theoretical Phys., Univ. of Cambridge, U.K.
47.
Nunes, R. A., and Simpson, J. H.(1985). “Axial convergence in a well-mixed estuary.”Estuarine, Coast. and Shelf Sci., 20(5), 637–649.
48.
O'Donnell, J.(1993). “Surface fronts in estuaries—a review.”Estuaries, 16(1), 12–39.
49.
Okubo, A.(1967). “The effect of shear in an oscillatory current on horizontal diffusion from an instantaneous source.”Int. J. Limnology and Oceanography, 1, 194–204.
50.
Okubo, A. (1973). “Effect of shoreline irregularities on streamwise dispersion in estuaries and other embayments.”Netherlands J. Sea Res., 6(1–2), 213–224.
51.
Oonishi, A., and Kunshi, H.(1979). “Water exchange between adjacent vortices under an additional oscillatory flow.”J. Oceanography Soc. Japan, 35, 136–140.
52.
Ottino, J. M. (1989). The kinematics of mixing: Stretching, chaos, and transport. Cambridge University Press, Cambridge, U.K.
53.
Park, J. K., and James, A. (1985). “Tidal variation of salt flux and dispersion in a polluted estuary.”Water Sci. and Technol., 17(6–7), 1001–1015.
54.
Pasmanter, R. (1988). “Deterministic diffusion, effective shear and patchiness in shallow tidal flows.”Physical processes in estuaries, J. Dronkers and W. van Leussen, eds., Springer-Verlag, New York, N.Y., 42–52.
55.
Postma, H.(1950). “The distribution of temperature and salinity in the Wadden Sea.”Tijdscr. K. ned. aardrijksk. Genoot., 67, 34–42.
56.
Pritchard, D. W.(1954). “A study of the salt balance in a coastal plain estuary.”J. Marine Res., 13, 133–144.
57.
Pritchard, D. W.(1956). “The dynamic structure of a coastal plain estuary.”J. Marine Res., 15, 33–42.
58.
Ridderinkhof, H., and Zimmerman, J. T. F.(1992). “Chaotic stirring in a tidal system.”Sci., 258(5085), 1107–1111.
59.
Ridderinkhof, H., Zimmerman, J. T. F., and Philippart, M. E.(1990). “Tidal exchange between the North-Sea and Dutch Wadden Sea and mixing time scales of the tidal basins.”Netherlands J. Sea Res., 25(3), 331–350.
60.
Schijf, J. B., and Schonfeld, J. C. (1953). “Theoretical considerations on the motion of salt and fresh water.”Proc., Minnesota Int. Hydr. Conf., Minneapolis, Minn., 321–333.
61.
Scott, C. F.(1993). “Canonical parameters for estuary classification.”Estuarine, Coast. and Shelf Sci., 36(6), 529–540.
62.
Scott, C. F.(1994). “A numerical study of the interaction of tidal oscillations and non-linearities in an estuary.”Estuarine Coastal and Shelf Sci., 39(5), 477–496.
63.
Shiono, K., and West, J. R.(1987). “Turbulent perturbations of velocity in the Conwy Estuary.”Estuarine Coast. and Shelf Sci., 25(5), 533–553.
64.
Signell, R. P., and Butman, B. (1992). “Modeling tidal exchange and dispersion in Boston Harbor.”J. Geophys. Res. Oc., 97(C10), 15,591–15,606.
65.
Signell, T. P., and Geyer, W. R. (1991). “Transient eddy formation around headlands.”J. Geophys. Res., 96(C2), 2561–2575.
66.
Smith, R.(1976). “Longitudinal dispersion of a buoyant contaminant in a shallow channel.”J. Fluid Mech., 78(4), 677–688.
67.
Smith, R.(1982a). “Contaminant dispersion in oscillatory flows.”J. Fluid Mech., 114, 379–398.
68.
Smith, R.(1982b). “Dispersion of tracers in the deep ocean.”J. Fluid Mech., 123, 131–142.
69.
Smith, R.(1983). “The contraction of contaminant distributions in reversing flows.”J. Fluid Mech., 129, 137–151.
70.
Smith, R.(1985). “When and where to put a discharge in an oscillatory flow.”J. Fluid Mech., 153, 479–599.
71.
Smith, R.(1993). “Optimum use of holding tanks to avoid pollution surges in narrow estuaries.”IMA J. Appl. Math., 51(2), 187–199.
72.
Smith, R. (1994). “A hydrodynamic derivation of an ADZ model for contaminant dispersion in estuary flows.”Mixing and Transport in the Environment, K. Beven, P. C. Chatwin, and P. Millbank, eds., Wiley, New York, N.Y., 371–382.
73.
Smith, R.(1995). “Distortion and dispersion: dilution of solutes in coastal waters.”Mixing in estuaries and coastal seas, C. Pattiaratchi, ed., 50, 479–495.
74.
Taylor, G. I.(1953). “Dispersion of soluble matter in solvent flowing slowly through a tube.”Proc., Royal Soc. of London, London, U.K., Series A, 219, 186–203.
75.
Thackson, E. L., and Schnelle, K. B.(1970). “Predicting effects of dead zones on stream mixing.”J. Sanit. Engrg. Div., ASCE, 96(2), 319–331.
76.
Townsend, A. A.(1951). “The diffusion of heat spots in isotropic turbulence.”Proc., Royal Soc. of London, London, U.K., Series A, 209, 418–430.
77.
Uncles, R. J., and Radford, P. J.(1980). “Seasonal and spring-neap tidal dependence of axial dispersion coefficients in the Severn—A wide, vertically mixed estuary.”J. Fluid Mech., 98(4), 703–726.
78.
Van Dam, G. C. (1994). “The study of shear dispersion in tidal waters by applying discrete particle techniques.”Mixing and Transport in the Environment, K. Beven, P. C. Chatwin, and P. Millbank, eds., Wiley, New York, N.Y., 269–293.
79.
Van de Kreeke, J., and Zimmerman, J. T. F. (1990). “Gravitational circulation in well and partially-mixed estuaries.”The Sea, B. LeMehaute, ed., Wiley, New York, N.Y.
80.
Van den Boogaard, H. F. P., Hoogkamer, M. J. J., and Heemink, A. W.(1993). “Parameter-identification in particle models.”Stochastic Hydrol. and Hydr., 7(2), 109–130.
81.
Webb, T., and Tomlinson, R. B.(1992). “Design procedures for effluent discharge to estuaries during ebb tide.”J. Envir. Engrg. Div., ASCE, 118(3), 338–362.
82.
West, J. R., Knight, D. W., and Shiono, K.(1985a). “A note on the determination of the vertical turbulent transport coefficients in a partially mixed estuary.”Proc., Instn. of Civ. Engrs., ICE, London, U.K., 79, 235–246.
83.
West, J. R., Knight, D. W., and Shiono, K.(1985b). “A note on the determination of the vertical turbulent transport coefficients in a partially mixed estuary.”Proc., Instn. of Civ. Engrs., ICE, London, U.K., 79, 235–246.
84.
West, J. R., Knight, D. W., and Shiono, K.(1986). “Turbulence measurements in the Great Ouse Estuary.”J. Hydr. Engrg., ASCE, 112(3), 167–180.
85.
West, J. R., and Mangat, J. S.(1986). “The determination and prediction of longitudinal dispersion coefficients in a narrow, shallow estuary.”Estuarine Coast. and Shelf Sci., 22(2), 161–181.
86.
West, J. R., and Shiono, K.(1985). “A note on turbulent perturbations of salinity in a partially mixed estuary.”Estuarine Coast. and Shelf Sci., 20(1), 55–78.
87.
West, J. R., Uncles, J. R., Stephens, J. A., and Shiono, K.(1990). “Longitudinal dispersion processes in the Upper Tamar Estuary.”Estuaries, 13(2), 118–124.
88.
Wood, T.(1979). “A modification of existing simple segmented tidal prism models of mixing in estuaries.”Estuarine and Coast. Marine Sci., 8, 339–347.
89.
Yasuda, H.(1982). “Longitudinal dispersion due to the boundary layer in an oscillating current—theoretical analysis in the case of an instantaneous line source.”J. Oceanographical Soc. of Japan, 38(6), 385–394.
90.
Yasuda, H.(1984). “Longitudinal dispersion of matter due to the shear effect of steady and oscillating currents.”J. Fluid Mech., 148, 383–403.
91.
Young, W. R., and Jones, S.(1991). “Shear dispersion.”Phys. of Fluids; A: Fluid Dyn., 3(5), 1087–1101.
92.
Young, W. R., Rhines, P. B., and Garrett, C. J. R.(1982). “Shear-flow dispersion, internal waves and horizontal mixing in the ocean.”J. Phys. Oceanography, 12(6), 515–527.
93.
Zimmerman, J. T. F. (1986). “The tidal whirlpool—A review of horizontal dispersion by tidal and residual currents.”Netherlands J. Sea Res., 20(2–3), 133–154.
94.
Zimmerman, J. T. F. (1988). “Estuarine residence times.”Hydrodynamics of estuaries, B. Kjerfve, ed., 75–84.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 123 • Issue 4 • April 1997
Pages: 332 - 340
Copyright
Copyright © 1997 American Society of Civil Engineers.
History
Published online: Apr 1, 1997
Published in print: Apr 1997
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.