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Vorticity and symplecticity in Lagrangian fluid dynamics

Bridges, T. J., Hydon, P. E. and Reich, Sebastien (2005) Vorticity and symplecticity in Lagrangian fluid dynamics Journal of Physics A: Mathematical and General, 38 (6). pp. 1403-1418.


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The relationship between potential vorticity (PV) and the symplectic form is explored, for the shallow-water equations governing Lagrangian particle paths. Starting with the symplectic form, the PV is found by the pullback operation to the reference space. At first sight, the encoding of PV in the symplectic form appears to be independent of the particle relabelling symmetry. The analysis is carried a step further in two ways. Using the ‘conservation of symplecticity’ as a starting point, the fluxes of symplecticity arise as differential forms, and a complete pull back of the flux forms leads to a geometric description of PV conservation. Secondly, symmetry methods are used to give a rigorous connection between particle relabelling, symplecticity and PV conservation. Generalizations of these issues to semi-geostrophic flow and three-dimensional Lagrangian fluid flows, and the connection with Ertel’s theorem are also discussed.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
Bridges, T.
Hydon, P.
Reich, Sebastien
Date : 11 February 2005
DOI : 10.1088/0305-4470/38/6/015
Uncontrolled Keywords : Lagrangian Fluid Dynamics, Vorticity and symplecticity
Additional Information : Thomas J Bridges et al 2005 J. Phys. A: Math. Gen. 38 1403-1418. This is a pre-copy-editing, author-prepared, peer-reviewed PDF of an article published in Journal of Physics A, 38, 1403-1418. © 2005 Institute of Physics Publishing Click here to access the publisher's version.
Depositing User : Mr Adam Field
Date Deposited : 27 May 2010 14:41
Last Modified : 16 Jan 2019 16:22

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