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New equations for nearly geostrophic flow

  • Rick Salmon (a1)

Abstract

I have used a novel approach based upon Hamiltonian mechanics to derive new equations for nearly geostrophic motion in a shallow homogeneous fluid. The equations have the same order accuracy as (say) the quasigeostrophic equations, but they allow order-one variations in the depth and Coriolis parameter. My equations exactly conserve proper analogues of the energy and potential vorticity, and they take a simple form in transformed coordinates.

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References

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Fofonoff, N. P. 1954 Steady flow in a frictionless homogeneous ocean. J. Mar. Res. 13, 254262.
Greene, J. M. 1982 Noncanonical Hamilton mechanics. Am. Inst. Phys. Proc. 88, 9197.
Hoskins, B. J. 1975 The geostrophic momentum approximation and the semi-geostrophic equations. J. Atmos. Sci. 32, 233242.
Lorenz, E. N. 1960 Energy and numerical weather prediction. Tellus 12, 364373.
Parsons, A. T. 1969 A two-layer model of Gulf Stream separation. J. Fluid Mech. 39, 511528.
Pedlosky, J. 1979 Geophysical Fluid Dynamics. Springer.
Phillips, N. A. 1963 Geostrophic motion. Rev. Geophys. 1, 123176.
Salmon, R. 1983 Practical use of Hamilton's principle. J. Fluid Mech. 132, 431444.
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New equations for nearly geostrophic flow

  • Rick Salmon (a1)

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