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A three-dimensional weakly nonlinear dynamics on tide-induced Lagrangian residual current and mass-transport

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Abstract

In recent years, studies of the environmental hydrodynamics in coastal seas and tidal estuaries have placed focus on the processes which determine the “fate” of longer-term transport. The lagrangian residual current has been recognized as an important factor which affects the longer term transport processes since it is more relevant to use a Lagrangian mean velocity rather than an Eulerian mean velocity to determine the origin of Water masses. In the present paper, an attempt is made to formulate a three-dimensional dynamics on the tideinduced Lagrangian residual current and mass-transport based upon a three-dimensional weakly-nonlinear model of tides. The Lagrangian residual velocity is shown to be the sum of the mass-transport velocity, which is the sum of the Eulerian residual velocity and the Stokes’ drift velocity, and the Lagrangian residual drift velocity which is dependent on the tidal current phase. This reveals that it is the mass-transport velocity which is the tidal cycle Eulerian mean of the Lagrangian residual velocity and that the mass-transport velocity is correct to the second order of approximation rather than to the first order. And then, a new longer-term transport equation which correctly describes the Lagrangian nature of transport processes without introducing the Fickian hypothesis for tidal dispersion is derived. In fact, the convection can be correctly represented by the Eulerian mean of the Lagrangian residual velocity, as the convective velocity in the longer-term transport equation is nothing but the mass-transport velocity.

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References

  1. Alfrink, B. J. and C. B. Vreugdenhil, 1981. Residual Currents. Rep. R. 1469-11, Delft Hydraul. Lab., Delft, The Netherlands, 32 pp.

    Google Scholar 

  2. Awaji, T., 1982. Water mixing in a tidal current and the effect of turbulence on tidal exchange through a strait.J. Physical Oceanogr. 12(6): 501–514.

    Article  Google Scholar 

  3. Bowden, K. F., 1965. Horizontal mixing in the sea due to a shearing current,J. Fluid Mech. 21: 83–95.

    Article  Google Scholar 

  4. Cheng, R. T., 1983. Euler-Lagrangian computation in estuarine hydrodynamics. Proc. Third Inter. Conf. on Num. Meth. in Laminar and Turbulent Flow, (Eds.), C. Taylor, J. A. Johnson and R. Smith, Pineridge Press, New York, pp. 341–352.

    Google Scholar 

  5. Cheng, R. T. and Casulli, V., 1982. On Lagrangian residual currents with applications in South San’ Francisco Bay, California.Water Resour. Res. 18(6): 1652–1662.

    Article  Google Scholar 

  6. Cheng, R. T. and Garther, J. W., 1984. Tides, tidal and residual currents in San Francisco Bay, California: results of measurements, 1979–1980. USGS Open-file Report, Rept. 84-xx, 120 pp.

  7. Dyer, K. R., 1973. Estuaries: a physical introduction. Wiley, London, pp. 140.

    Google Scholar 

  8. Dyer, K. R., 1974. The salt balance in stratified estuaries.Estuarine and Coastal Marine Science 2: 273–281.

    Article  Google Scholar 

  9. Elliott, A. J. and T. E. Hendrix, 1976. Intensive observations of the circulation in the Potomac estuary. Chesapeake Bay Institute, Sepc. Rept., No. 55, 35 pp.

  10. Feng Shizuo, 1982. Numerical Models Adopted in the East China Sea Studies and the Preliminary Results of Their Application to General Circulation, Tides, Storm Surges and Pollutant Dispersion. Proceedings of J. O. A., Abstracts of the Poster Sessions (microfiche), Dalhousie Univ., Halifax, Nova Scotia, Canada.

  11. Feng, Shih-zao (Feng Shizuo), 1977. A three-dimensional non-linear model of tides.Scientia Sinica 20 (4): 436–446.

    Google Scholar 

  12. Feng Shizuo and Sun Wenxin, 1983. A tidal three-dimensional non-linear model with variable eddy viscosity.Chinese J. of Oceanology & Limnology 1(2): 166–170.

    Article  Google Scholar 

  13. Fischer, H. B., 1976. Mixing and dispersion in estuaries,Ann. Rev. Fluid Mech 8: 107–133.

    Article  Google Scholar 

  14. Fischer, H. B. et al., 1979. Mixing in inland and coastal waters. Academic Press, N. Y., 483 pp.

    Google Scholar 

  15. Heaps, N. S., 1978. Linearized vertically-integrated equations for residual circulation in coastal seas.Deut. Hydrog. Z. 31: 147–169.

    Article  Google Scholar 

  16. Leendertse, J. J., 1970. A water-quality simulation model for well-mixed estuaries and coastal seas. Vol. 1, Principles of Computation, Rep. RM-6230-R6, Rand Corp., Santa Monica, California.

    Google Scholar 

  17. Leendertse, J. J. and Gritton, E. C., 1971. Vol. II, Computation Procedures; Vol. III, Jamaica Bay Simulation, Rep. R-708-NUC and R-709-NYC, Rand Corp. Santa Monica, California.

    Google Scholar 

  18. Lewis, R. E. and J. O. Lewis, 1983. The principal factors contributing to the flux of salt in a narrow, partially stratified estuary.Estuarine, Coastal and Marine Science 16: 599–626.

    Article  Google Scholar 

  19. Longuet-Higgins, M. S., 1969. On the transport of mass by time-varying ocean currents.Deep Sea Res. 16: 431–447.

    Google Scholar 

  20. Pritchard, D. W., 1954. A study on the salt balance in a coastal plain estuary.J. Mar. Res. 13: 133–144.

    Google Scholar 

  21. Stern, M. E., 1975. Ocean Circulation Physics. Academic Press, New York, 246 pp.

    Google Scholar 

  22. Stommel, H. and H. G. Farmer, 1952. On the nature of estuarine circulation, Part I. Reference 52–88. Woods Hole Oceanographic Institution, Woods Hole, Massachusetts.

    Book  Google Scholar 

  23. Sun Wenxin, Chen Zongyong and Feng Shizuo, 1981. Numerical simulation of three-dimensional non-linear tidal waves (I)—A numerical study for M4 and MS4 waves in the Bohai Sea.J. Shandong College of Oceanology 11(1): 23–31. (In Chinese with English abstract)

    Google Scholar 

  24. Sung Lina, 1986a. A Hydrodynamic Velocity-splitting Model with a Depth-varying Eddy viscosity in Shallow Seas (I)—The Velocity-splitting Model.J. Shandong College of Ocean.16(2).

  25. Sung Lina, 1986b. A Hydrodynamic Velocity-splitting Model with a Depth-varying Eddy viscosity in Shallow Seas (II)—An application of the velocity-splitting Model to the Zeroth-order Model of the Ultra-shallow water storm surges.J. Shandong College of Ocean.16(3). (In Chinese with English abstract)

  26. Tee, T. K., 1976. Tide-induced residual current: A 2-D non-linear numerical model.J. Mar. Res. 31: 603–628.

    Google Scholar 

  27. Uncles, R. J. and M. B. Jordan, 1979. Residual fluxes of water and salt at two stations in the Severn estuary.Estuarine and Coastal Marine Science 9: 287–302.

    Article  Google Scholar 

  28. Uncles, R. J. and M. B. Jordan, 1980. A one-dimensional representation of residual currents in the Severn estuary and associated observations.Estuarine and Coastal Marine Science 10: 39–60.

    Article  Google Scholar 

  29. Uncles, R. J. and P. J. Radford, 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.

    Article  Google Scholar 

  30. Weisberg, R. H., 1976. The nontidal flow in the Providence River of Narragansen Bavi A slochastic approach to estuarne eireulation.J. Phys. Oceanogr. 6: 721–734.

    Article  Google Scholar 

  31. Winterwerp, J. C., 1983. Decomposition of the mass transport in narrow estuaries.Fstuarine. Coastal and Shelf Science 16: 627–638.

    Article  Google Scholar 

  32. Yu Guangvao and Chen Shijun. 1983. Numerical modeling of the cireulation and pollutant dispersion in Jiaozhou Bay (III)—the Lagrangian residual current and the pollutant dispersion.J. Shandong College of Oceanology 13(1): 1–14. (In Chinese with English abstract)

    Google Scholar 

  33. Zimmerman, J. T. F., 1978. Dispersion by tide-induced residual current vortices. Hydrodynamics of Estuaries and Fjords, (Ed.) J. C. J. Nihoul, Elsevier Scientific Publishing Co., N. Y., pp. 207–216.

    Google Scholar 

  34. Zimmerman, J. T. F., 1979. On the Euler-Lagrangian transformation and the Stokes drift in the presence of oscillatory and residual currents.Deep Sea Res. 26A: 505–520.

    Google Scholar 

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Authors and Affiliations

  1. Shandong College of Oceanology, Shandong, China

    Feng Shizuo

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  1. Feng Shizuo
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Submitted for IAMAP/IAPSO Joint Assembly, August 5–16, 1985, Honolulu, Hawaii U.S.A.

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Shizuo, F. A three-dimensional weakly nonlinear dynamics on tide-induced Lagrangian residual current and mass-transport. Chin. J. Ocean. Limnol. 4, 139–158 (1986). https://doi.org/10.1007/BF02850431

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  • DOI: https://doi.org/10.1007/BF02850431

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