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144 A Semi-Implicit, Three-Dimensional Model for Estuarine Circulation for both the two-level and three-level schemes can be extended by using iteration, although the number of iterations should be kept to a minimum because iteration in three dimensions is expensive. Using more than one iteration of the trapezoidal step in the three- level scheme or more than two iterations in the two-level scheme was not worthwhile for the 1-D test experiments, considering the extra computational expense incurred for minimal improvement in accuracy; in the few instances when extra iterations were needed to stabilize a particular solution, the values for the time step and Courant numbers were too large anyway to retain needed accuracy. Although more testing of the 3-D, semi-implicit scheme is necessary, the results from the seiching experiment look promising. Accurate results are obtained for time steps that exceed the CFL condition for the gravity waves. Mass preservation is excellent. Because of the implicit nature of the numerical scheme, some phase errors do appear in solutions having large time steps. However, it is unlikely that this source of error will be prevalent in real tidal simulations of estuaries. If it is, it can at least be minimized by the use of the trapezoidal step in the scheme. 7. References Abbott, M.B., and Ionescu, F., 1967, On the numerical computation of nearly-horizontal flows: Journal of Hydraulic Research, v. 5, no. 2, p. 97−117. Abraham, Gerrit, 1988, Turbulence and mixing in stratified tidal flows, in Dronkers, J.J., and van Leussen, Wim, eds., Physical processes in estuaries: Berlin, Germany, Springer, p. 149−180. Adams, C.E., and Weatherly, G.L., 1981, Suspended-sediment transport and benthic boundary-layer dynamics: Marine Geology, v. 42, p. 1−18. Amein, M.M., and Fang, C.S., 1970, Implicit flood routing in natural channels: American Society of Civil Engineers, Journal of the Hydraulics Division, v. 96, no. 12, p. 2481−2500. American Society of Civil Engineers, 1988, Turbulence modeling of surface water flow and transport—Part I, Prepared by the Task Committee on Turbulence Models in Hydraulic Computations: American Society of Civil Engineers, Journal of Hydraulic Engineering, v. 114, no. 9, p. 970−991. Ames, W.F., 1977, Numerical methods for partial differential equations (2nd ed.): New York, Academic Press, 365 p. Asselin, R., 1972, Frequency filters for time integrations: American Meteorological Society, Monthly Weather Review, v. 100, p. 487−490. Axelsson, O., and Lindskog, G., 1986, On the eigenvalue distribution of a class of preconditioning methods: Numerical Mathematics, v. 48, p. 479−498. Backhaus, J.O., 1983, A semi-implicit scheme for the shallow water equations for application to shelf sea modeling: Continental Shelf Research, v. 2, no. 4, p. 243−254. Backhaus, J.O., 1985, A three-dimensional model for the simulation of shelf sea dynamics: Deutsche Hydrographische Zeitschrift [German Hydrographic Newspaper], v. 38, p. 165−187. Bedford, K.W., Dingman, J.S., and Yeo, W.K., 1987, Preparation of estuary and marine model equations by generalized filtering methods, in Nihoul, J.C.J., and Jamart, B.M., eds., Three-dimensional models of marine and estuarine dynamics: Amsterdam, Netherlands, Elsevier, p. 113−125. Beer, F.P., and Johnston, E.R., 1962, Vector mechanics for engineers—statics and dynamics: New York, McGraw-Hill, 781 p.
7. References 145 Benqué, J.P., Cunge, J.A., Feuillet, Jacques, Hauguel, Alain, and Holly, F.M., 1982, New method for tidal current computation: American Society of Civil Engineers, Journal of the Waterway, Port, Coastal, and Ocean Division, v. 108, no. 3, p. 396−417. Berger, R.C., Martin, W.D., McAdory, R.T., and Schmidt, J.H., 1994, Galveston Bay 3D model study, channel deepening, circulation, and salinity results, Proceedings of the Third Estuarine and Coastal Modeling Conference: American Society of Civil Engineers, Oak Brook, Ill., September 8−10, 1993, p. 1−13. Berger, R.C., McAdory, R.T., Schmidt, J.H., Martin, W.D., and Hauck, L.H., 1995, Houston−Galveston navigation channels, Texas project—Report 4, three-dimensional numerical modeling of hydrodynamics and salinity: U.S. Army Corps of Engineers Waterways Experiment Station, Vicksburg, Miss., Technical Report HL-92-7, 29 p., 425 plus. Blake, R.A., 1991, The dependence of wind stress on wave height and wind speed: American Geophysical Union, Journal of Geophysical Research (Oceans), v. 96, no. C11, p. 20531−20545. Bleck, Rainer, and Boudra, D.B., 1981, Initial testing of a numerical ocean circulation model using a hybrid (quasi-isopycnic) vertical coordinate: American Meteorological Society, Journal of Physical Oceanography, v. 11, no. 6, p. 755−770. Bleck, Rainer, and Boudra, D.B., 1986, Wind-driven spin-up in eddy-resolving ocean models formulated in isopycnic and isobaric coordinates: American Geophysical Union, Journal of Geophysical Research (Oceans), v. 91, no. C6, p. 7,611−7,621. Blumberg, A.F., 1977, Numerical model of estuarine circulation: American Society of Civil Engineers, Journal of the Hydraulics Division, v. 103, no. 3, p. 295−310. Blumberg, A.F., 1986, Turbulent mixing processes in lakes, reservoirs, and impoundments; Chapter 4 in Gray, W.G., ed., Physics- based modeling of lakes, reservoirs, and impoundments: American Society of Civil Engineers, p. 79−104. Blumberg, A.F., 1991, A primer for ECOM-si [Estuarine Coastal and Ocean Model-semi-implicit]: Hydrator, Inc., Mahwah, N.J., Prepared for the U.S. Geological Survey, 68 p. Blumberg, A.F., and Galperin, Boris, 1990, On the summer circulation in New York Bight and contiguous estuarine waters, in Cheng, R.T., ed., Residual currents and long-term transport: New York, Springer, Coastal and Estuarine Studies, v. 38, p. 451−468. Blumberg, A.F., and Goodrich, D.M., 1990, Modeling of wind induced destratification in Chesapeake Bay: Estuaries, v. 13, p. 1236−1249. Blumberg, A.F., and Herring, H.J., 1987, Circulation modeling using orthogonal curvilinear coordinates, in Nihoul, J.C.J., and Jamart, B.M., eds., Three-dimensional models of marine and estuarine dynamics: Amsterdam, Netherlands, Elsevier, p. 55−88. Blumberg, A.F., and Mellor, G.L., 1980, A coastal ocean numerical model, in Sündermann, Jürgen, and Holz, K.-P., eds., Lecture notes on coastal and estuarine studies—mathematical modelling of estuarine physics: Proceedings of an International Symposium held at the German Hydrographic Institute, Hamburg, August 24−26, 1978, Berlin, Germany, Springer, p. 203−219. Blumberg, A.F., and Mellor, G.L., 1987, A description of a three-dimensional coastal ocean circulation model, in Heaps, N.S., ed., Three-dimensional coastal ocean models: American Geophysical Union, Washington, D.C., Coastal and Estuarine Sciences Monograph Series, v. 4, p. 1−16. Blumberg, A.F., Signell, R.P., and Jenter, H.L., 1993, Modeling transport processes in the coastal ocean: Journal of Marine Environmental Engineering, v. 1, no. 1, p. 31−52.
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In cooperation with the Interagency
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U.S. Department of the Interior Dir
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vi 4.2 Semi-Implicit One-Dimensiona
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viii Figure 5.6. Graph showing solu
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x Tables Table 2.1. Dimensionless n
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2 A Semi-Implicit, Three-Dimensiona
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2.4.1.2 Dynamic Surface Condition 2
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Water surface Water surface Level p
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h 1 h 2 h 3 h 4 h 5 h 6 z 1 ⁄ 2 z
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