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Holomorphic structures in hydrodynamical models of nearly geostrophic flow

Roubtsov, VN and Roulstone, I (2001) Holomorphic structures in hydrodynamical models of nearly geostrophic flow PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 457 (2010). 1519 - 1531. ISSN 1364-5021

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Abstract

We study complex structures arising in Hamiltonian models of nearly geostrophic flows in hydrodynamics. In many of these models an elliptic Monge-Ampère equation defines the relationship between a 'balanced' velocity field, defined by a constraint in the Hamiltonian formalism, and the materially conserved potential vorticity. Elliptic Monge-Ampère operators define an almost-complex structure, and in this paper we show that a natural extension of the so-called geostrophic momentum transformation of semi-geostrophic theory, which has a special importance in theoretical meteorology, defines Kahler and special Kähler structures on phase space. Furthermore, analogues of the 'geostrophic momentum coordinates' are shown to be special Lagrangian coordinates under conditions which depend upon the physical approximations under consideration. Certain duality properties of the operators are studied within the framework of the Kähler geometry.

Item Type: Article
Uncontrolled Keywords: Science & Technology, Multidisciplinary Sciences, Science & Technology - Other Topics, holomorphic function, Hamiltonian structure, hydrodynamics, Kahler geometry, special Lagrangian coordinates, Monge-Ampere equations, MONGE-AMPERE EQUATIONS, CONTACT TRANSFORMATIONS, SEMIGEOSTROPHIC THEORY, INTERMEDIATE MODELS, GEOMETRY
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Divisions: Faculty of Engineering and Physical Sciences > Mathematics
Depositing User: Mr Adam Field
Date Deposited: 27 May 2010 14:41
Last Modified: 23 Sep 2013 18:33
URI: http://epubs.surrey.ac.uk/id/eprint/1533

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