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Large-scale semigeostrophic equations for use in ocean circulation models

Published online by Cambridge University Press:  26 April 2006

Rick Salmon
Rick Salmon
Affiliation:
Scripps Institution of Oceanography, University of California San Diego, La Jolla, CA 92093-0225, USA
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Abstract

Hamiltonian approximation methods yields approximate dynamical equations that apply to nearly geostrophic flow at scales larger than the internal Rossby deformation radius. These equations incorporate fluid inertia with the same order of accuracy as the semi-geostrophic equations, but are nearly as simple (in appropriate coordinates) as the equations obtained by completely omitting the inertia.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 318 , 10 July 1996 , pp. 85 - 105
Copyright
© 1996 Cambridge University Press

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References

Allen, J. S., Barth, J. A. & Newberger, P. A. 1990 On intermediate models for barotropic continental shelf and slope flow fields. Part I: Formulation and comparison of exact solutions. J. Phys. Oceanogr. 20, 1017–1042.Google Scholar
Cullen, M. J. P., Norbury, J. & Purser, R. J. 1991 Generalized Lagrangian solutions for atmospheric and oceanic flows. SIAM J. Appl. Maths 51, 20–31.Google Scholar
Cullen, M. J. P. & Purser, R. J. 1984 An extended theory of semi-geostrophic frontogenesis. J. Atmos. Sci. 41, 1477–1497.Google Scholar
Cullen, M. J. P. & Purser, R. J. 1989 Properties of the Lagrangian semigeostrophic equations. J. Atmos. Sci. 46, 2684–2697.Google Scholar
Hoskins, B. J. 1975 The geostrophic momentum approximation and the semigeostrophic equations. J. Atmos. Sci. 32, 233–242.Google Scholar
McWilliams, J. C. & Gent, P. R. 1980 Intermediate models of planetary circulations in the atmosphere and ocean. J. Atmos. Sci. 37, 1657–1678.Google Scholar
Purser, R. J. 1993 Contact transformations and Hamiltonian dynamics in generalized semigeostrophic theories. J. Atmos. Sci. 50, 1449–1468.Google Scholar
Salmon, R. 1983 Practical use of Hamilton's principle. J. Fluid Mech. 132, 431–444.Google Scholar
Salmon, R. 1985 New equations for nearly geostrophic flow. J. Fluid Mech. 153, 461–477.Google Scholar
Salmon, R. 1988a Semigeostrophic theory as a Dirac-bracket projection. J. Fluid Mech. 196, 345–358.Google Scholar
Salmon, R. 1988b Hamiltonian fluid mechanics. Ann. Rev. Fluid Mech. 20, 225–256.Google Scholar
Salmon, R. 1994 Generalized two-layer models of ocean circulation. J. Mar. Res. 52, 865–908.Google Scholar
Shutts, G. J. 1989 Planetary semi-geostrophic equations derived from Hamilton's principle. J. Fluid Mech. 208, 545–573.Google Scholar
Shutts, G. J., Cullen, M. J. P. & Chynoweth, S. 1987 Parcel stability and its relation to semigeostrophic theory. J. Atmos. Sci. 44, 1318–1330.Google Scholar
Shutts, G. J., Cullen, M. J. P. & Chynoweth, S. 1988 Geometric models of balanced semigeostrophic flow. Annal. Geophys. 6, 493–500.Google Scholar