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An alternative view of generalized Lagrangian mean theory

Published online by Cambridge University Press:  19 February 2013

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

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.

JFM classification

Mathematical Foundations: Mathematical Foundations Mathematical Foundations: Variational methods Geophysical and Geological Flows: Waves in rotating fluids
Type
Papers
Information
Journal of Fluid Mechanics , Volume 719 , 25 March 2013 , pp. 165 - 182
Copyright
©2013 Cambridge University Press

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