Publications

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2014
Salmon, R.  2014.  Analogous formulation of electrodynamics and two-dimensional fluid dynamics. Journal of Fluid Mechanics. 761   10.1017/jfm.2014.642   AbstractWebsite

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.

2013
Salmon, R.  2013.  An alternative view of generalized Lagrangian mean theory. Journal of Fluid Mechanics. 719:165-182.   10.1017/jfm.2012.638   AbstractWebsite

If the variables describing wave-mean flow interactions are chosen to include a set of fluid-particle labels corresponding to the mean flow, then the generalized Lagrangian mean (GLM) theory takes the form of an ordinary classical field theory. Its only truly distinctive features then arise from the distinctive feature of fluid dynamics as a field theory, namely, the particle-relabelling symmetry property, which corresponds by Noether's theorem to the many vorticity conservation laws of fluid mechanics. The key feature of the formulation is that all the dependent variables depend on a common set of space-time coordinates. This feature permits an easy and transparent derivation of the GLM equations by use of the energy-momentum tensor formalism. The particle-relabelling symmetry property leads to the GLM potential vorticity law in which pseudo-momentum is the only wave activity term present. Thus the particle-relabelling symmetry explains the prominent importance of pseudo-momentum in GLM theory.