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Analogous formulation of electrodynamics and two-dimensional fluid dynamics

Published online by Cambridge University Press:  18 November 2014

Rick Salmon
Rick Salmon*
Affiliation:
Scripps Institution of Oceanography, University of California, San Diego, La Jolla,CA 92093-0213, USA
*
†Email address for correspondence: [email protected]
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Abstract

A single, simply stated approximation transforms the equations for a two-dimensional perfect fluid into a form that is closely analogous to Maxwell’s equations in classical electrodynamics. All the fluid conservation laws are retained in some form. Waves in the fluid interact only with vorticity and not with themselves. The vorticity is analogous to electric charge density, and point vortices are the analogues of point charges. The dynamics is equivalent to an action principle in which a set of fields and the locations of the point vortices are varied independently. We recover classical, incompressible, point vortex dynamics as a limiting case. Our full formulation represents the generalization of point vortex dynamics to the case of compressible flow.

JFM classification

Mathematical Foundations: Mathematical Foundations Vortex Flows: Vortex dynamics
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 761 , 25 December 2014 , R2
Copyright
© 2014 Cambridge University Press 

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