Abstract
The ocean contains motions on many scales. In all numerical models it is necessary to parameterize the effect of unresolved scales of motion by some smoothing, usually in the form of Laplacian friction. This leads to equations which are both hyperbolic and parabolic. In this chapter we study simple diffusion equations in order to learn how to formulate the diffusive part of the problem and how to investigate the linear numerical stability of finite difference schemes. All methods are not stable.
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References
Charney, J., Geostrophic Turbulence, J. Atmos. Sci., 28, 1087–1095, 1977.
Crowley, W. P., A global numerical model: Part 1, J. Comp. Phys., 3, 111–147, 1968.
Deardorff, J. W., A three-dimensional numerical investigation of the idealized planetary boundary layer, Geophys. Fluid Dynamics, 1, 377–410, 1970.
Deardorff, J. W., On the magnitude of the subgrid scale eddy coefficient, J. Comp. Phys., 7, 120–133, 1971.
DuFort, E. C., and Frankel, S. P., Stability conditions in the numerical treatment of parabolic differential equations, Math Tables and Other Aids to Computations, 7, 135–152, 1953.
Haney, R., The relationship between the grid size and the coefficient of nonlinear lateral eddy viscosity in numerical ocean circulation models, J. Comp. Phys., 19, 257–266, 1975.
Leith, C. E., Two dimensional eddy viscosity coefficients, Proc. WMO/IUGG Symposium on Numerical Weather Prediction, Tokyo, Japan, Nov. 26-Dec. 4, 1968, I-41-I-44, 1968.
Lilly, D. K., The representation of small-scale turbulence in numerical simulation experiments, Proc. IBM Scientific Computing Symposium on Environmental Sciences, 195–210, 1967.
O’Brien, J. J., A two-dimensional model of the wind-driven North Pacific, Inves. Pesq., 35(1), 331-349, 1971.
Ogura, Y., Convection of isolated masses of a buoyant fluid, J. Atmos. Sci., 19, 492–502, 1962.
Phillips, N. A., An example of nonlinear computational instability, The Atmosphere and The Sea in Motion: Rossby Memorial Volume, Rockefeller Institute Press, New York, 501–504, 1959.
Richtmyer, R. D., and Morton, K. W., Difference Methods for Initial Value Problems, 406 pp., Interscience, New York, 1967.
Smagorinsky, J., General circulation experiments with the primitive equations, I. The basic experiment, Mon. Wea. Rev., 91, 99–164, 1963.
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© 1986 Springer Science+Business Media Dordrecht
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O’Brien, J.J. (1986). The Diffusive Problem. In: O’Brien, J.J. (eds) Advanced Physical Oceanographic Numerical Modelling. NATO ASI Series, vol 186. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0627-8_9
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DOI: https://doi.org/10.1007/978-94-017-0627-8_9
Publisher Name: Springer, Dordrecht
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