Analogous formulation of electrodynamics and two-dimensional fluid dynamics

TitleAnalogous formulation of electrodynamics and two-dimensional fluid dynamics
Publication TypeJournal Article
Year of Publication2014
AuthorsSalmon R
JournalJournal of Fluid Mechanics
Volume761
Date Published2014/12
Type of ArticleArticle
ISBN Number0022-1120
Accession NumberWOS:000351134000002
Keywordsmathematical foundations; model; sound; vortex; vortex dynamics; wave-turbulence interactions; waves
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.

DOI10.1017/jfm.2014.642
Short TitleJ. Fluid Mech.
Student Publication: 
No