, Volume 118, Issue 1, pp 152-176

An introduction to the generalized Lagrangian-mean description of wave, mean-flow interaction

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Abstract

The generalized Lagrangian-mean description is motivated and illustrated by means of some simple examples of interactions between waves and mean flows, confining attention for the most part to waves of infinitesimal amplitude. The direct manner in which the theoretical description leads to the wave-action concept and related results, and also to the various ‘noninteraction’ theorems, more accuratelynon-acceleration theorems, is brought out as simply as possible. Variational formulations are not needed in the analysis, which uses elementary principles only.

The significance of the generalized Eliassen-Palm relations as conservation equations for wave activity is discussed briefly, as is the significance of the temporal nonuniformity of the generalized Lagrangian-mean description for dissipating disturbances.

This review article, is based on material prepared for a summer colloquium on ‘The General Circulation: Theory, Modeling, and Observations’ held at the National Center for Atmospheric Research in July 1978 and sponsored by the Advanced Study Program.
The National Center for Atmospheric Research is sponsored by the National Science Foundation.