Abstract
The design of numerical models is introduced through an analysis of the stability of finite difference approximations of the shallow-water equations. An outline of nonlinear instability, and methods to control it, is followed by a discussion of vertical coordinate systems, and examples of the application of models of various design to the investigation of the large scale potential vorticity pattern in the main thermocline.
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References
Cox, M.D., (1985): An eddy-resolving numerical model of the ventilated thermodine. J. Phys. Oceanogr., 15, 1312–1334.
Cox, M.D., (1987): Isopycnal diffusion in a z-coordinate ocean model. Ocean Modelling, 74, 1–5.
Holland, W.R., T. Keffer, and P.B. Rhines, (1984): Dynamics of the oceanic general circulation: The potential vorticity field. Nature, 308, 698–705.
Huang, R.X., and K. Bryan, (1987): A multilayer model of the thermohaline and wind-driven ocean circulation.J. Phys. Oceanogr. 17, 1909–1924.
Keffer, T., (1985): The ventilation of the world’s oceans: Maps of the potential vorticity field. J. Phys. Oceanogr., 15, 509–523.
Luyten, J.R., J. Pedlosky, and H. Stommel, (1983): The ventilated thermocline. J. Phys. Oceanogr., 13, 292–309.
Mesinger, F., and A. Arakawa, (1976): Numerical Methods Used in Atmospheric Models. Global Atmospheric Res. Program Publ. No. 17, World Met. Organ., Geneva, 64 pp.
Moore, D., and S.G.H. Philander, (1977): Modelling of the tropical oceanic circulation. The Sea, 6, Wiley, 319–361.
National Academy of Science (U.S.), (1975): Numerical Models of Ocean Circulation. Washington, D.C., 364 pp.
O’Brien, J.J., (1986): Advanced Physical Oceanographic Modelling, Edited by J.J. O’Brien, D. Reidel, 608 pp.
Pedlosky, J., (1987): Geophysical Fluid Dynamics, 2nd Ed., Springer-Verlag, Berlin, New York, 710 p.
Phillips, N.A., (1956): The general circulation of the atmosphere: a numerical experiment. Quart. J. Roy. Meteor. Soc. 82, 123–164.
Phillips, N.A., (1959): An example of non-linear computational instability. The Atmosphere and the Sea in Motion, Rossby Memorial Volume, New York, Rockefeller Inst. press, 501–504.
Redi, M.H., (1982): Oceanic isopycnal mixing by coordinate rotation. J. Phys. Oceanogr., 12, 1154–1158.
Richtmeyer, R.D., and K.W. Morton, (1967): Difference Methods for Initial Value Problems. New York, Interscience, 406 pp.
Veronis, G., (1975): The role of models in tracers studies. In Numerical models of ocean circulation. Nat. Acad. of Sciences, Washington, D.C., 133–146.
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© 1989 Kluwer Academic Publishers
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Bryan, K. (1989). The Design of Numerical Models of the Ocean Circulation. In: Anderson, D.L.T., Willebrand, J. (eds) Oceanic Circulation Models: Combining Data and Dynamics. NATO ASI Series, vol 284. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-1013-3_15
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DOI: https://doi.org/10.1007/978-94-009-1013-3_15
Publisher Name: Springer, Dordrecht
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