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A Hamiltonian structure with contact geometry for the semi-geostrophic equations

Published online by Cambridge University Press:  26 April 2006

I. Roulstone  and
J. Norbury
I. Roulstone
Affiliation:
Forecasting Research Division, Meteorological Office, London Road, Bracknell, Berkshire, RG12 2SZ, UK
J. Norbury
Affiliation:
Mathematical Institute, 24–29 St. Giles, Oxford, OX1 3LB, UK
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Abstract

A canonical Hamiltonian structure for the semi-geostrophic equations is presented and from this a reduced non-canonical Hamiltonian structure is derived, providing a fully nonlinear version of the approximate linearized vorticity advection representation. The structure of this model is described naturally within the framework of contact geometry. A Hamiltonian approach leading to a symplectic algorithm for calculating solutions to the equations of motion is formulated. Basic necessary functional methods are introduced and the Lagrangian and Eulerian kinematic structures are discussed, together with their relevance to symplectic integrating algorithms.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 272 , 10 August 1994 , pp. 211 - 234
Copyright
Copyright © Cambridge University Press 1994

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