On non-dissipative wave-mean interactions in the atmosphere or oceans

Oliver Buhler, Michael E. McIntyre

Research output: Contribution to journalArticle

Abstract

Idealized model examples of non-dissipative wave-mean interactions, using small-amplitude and slow-modulation approximations, are studied in order to re-examine the usual assumption that the only important interactions are dissipative. The results clarify and extend the body of wave-mean interaction theory on which our present understanding of, for instance, the global-scale atmospheric circulation depends (e.g. Holton et al. 1995). The waves considered are either gravity or inertia-gravity waves. The mean flows need not be zonally symmetric, but are approximately 'balanced' in a sense that non-trivially generalizes the standard concepts of geostrophic or higher-order balance at low Froude and/or Rossby number. Among the examples studied are cases in which irreversible mean-flow changes, capable of persisting after the gravity waves have propagated out of the domain of interest, take place without any need for wave dissipation. The irreversible mean-flow changes can be substantial in certain circumstances, such as Rossby-wave resonance, in which potential-vorticity contours are advected cumulatively. The examples studied in detail use shallow-water systems, but also provide a basis for generalizations to more realistic, stratified flow models. Independent checks on the analytical shallow-water results are obtained by using a different method based on particle-following averages in the sense of 'generalized Lagrangian-mean theory', and by verifying the theoretical predictions with nonlinear numerical simulations. The Lagrangian-mean method is seen to generalize easily to the three-dimensional stratified Boussinesq model, and to allow a partial generalization of the results to finite amplitude. This includes a finite-amplitude mean potential-vorticity theorem with a larger range of validity than had been hitherto recognized.

Original languageEnglish (US)
Pages (from-to)301-343
Number of pages43
JournalJournal of Fluid Mechanics
Volume354
StatePublished - Jan 10 1998

Fingerprint

oceans
atmospheres
Gravity waves
Vorticity
interactions
shallow water
gravity waves
vorticity
Water
stratified flow
Gravitation
atmospheric circulation
Modulation
planetary waves
inertia
Computer simulation
dissipation
theorems
gravitation
modulation

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Physics and Astronomy(all)
  • Condensed Matter Physics

Cite this

On non-dissipative wave-mean interactions in the atmosphere or oceans. / Buhler, Oliver; McIntyre, Michael E.

In: Journal of Fluid Mechanics, Vol. 354, 10.01.1998, p. 301-343.

Research output: Contribution to journalArticle

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