Monge-Ampère Structures and the Geometry of Incompressible Flows

Banos, B, Roubtsov, V and Roulstone, I (2016) Monge-Ampère Structures and the Geometry of Incompressible Flows Journal of Physics A: Mathematical and Theoretical, 49 (24).

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Abstract

We show how a symmetry reduction of the equations for incompressible hydrodynamics in three dimensions leads naturally to Monge-Ampere structure, and Burgers’-type vortices are a canonical class of solutions associated with this structure. The mapping of such solutions, which are characterised by a linear dependence of the third component of the velocity on the coordinate defining the axis of rotation, to solutions of the incompressible equations in two dimensions is also shown to be an example of a symmetry reduction. The Monge-Ampere structure for incompressible flow in two dimensions is shown to be hyper-symplectic.

Item Type:	Article
Subjects :	subj_Mathematics
Divisions :	Faculty of Engineering and Physical Sciences > Mathematics
Authors :	Name Email ORCID Banos, B Roubtsov, V Roulstone, I
Date :	11 May 2016
DOI :	10.1088/1751-8113/49/24/244003
Copyright Disclaimer :	This is an author-created, un-copyedited version of an article published in Journal of Physics A: Mathematical and Theoretical.. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at http://dx.doi.org/10.1088/1751-8113/49/24/244003
Depositing User :	Symplectic Elements
Date Deposited :	12 May 2016 10:54
Last Modified :	12 May 2017 02:08
URI:	http://epubs.surrey.ac.uk/id/eprint/810684

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