An alternative view of generalized Lagrangian mean theory

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

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flow interaction, fluid, mathematical foundations, variational methods, wave-action, waves in rotating fluids


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.