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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Gao, Shouting and Ran, Lingkun 2009. Diagnosis of wave activity in a heavy‐rainfall event. Journal of Geophysical Research, Vol. 114, Issue. D8,


    Bühler, Oliver 2010. Wave–Vortex Interactions in Fluids and Superfluids. Annual Review of Fluid Mechanics, Vol. 42, Issue. 1, p. 205.


    Bühler, Oliver 2014. A gentle stroll through EP flux theory. European Journal of Mechanics - B/Fluids, Vol. 47, p. 12.


    Nault, Joshua T. and Sutherland, Bruce R. 2008. Beyond ray tracing for internal waves. I. Small-amplitude anelastic waves. Physics of Fluids, Vol. 20, Issue. 10, p. 106601.


    ACHATZ, ULRICH KLEIN, R. and SENF, F. 2010. Gravity waves, scale asymptotics and the pseudo-incompressible equations. Journal of Fluid Mechanics, Vol. 663, p. 120.


    Shaw, Tiffany A. and Shepherd, Theodore G. 2009. A Theoretical Framework for Energy and Momentum Consistency in Subgrid-Scale Parameterization for Climate Models. Journal of the Atmospheric Sciences, Vol. 66, Issue. 10, p. 3095.


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  • Journal of Fluid Mechanics, Volume 594
  • January 2008, pp. 493-506

Wave-activity conservation laws for the three-dimensional anelastic and Boussinesq equations with a horizontally homogeneous background flow

  • TIFFANY A. SHAW (a1) and THEODORE G. SHEPHERD (a1)
  • DOI: http://dx.doi.org/10.1017/S0022112007009160
  • Published online: 10 January 2008
Abstract

Wave-activity conservation laws are key to understanding wave propagation in inhomogeneous environments. Their most general formulation follows from the Hamiltonian structure of geophysical fluid dynamics. For large-scale atmospheric dynamics, the Eliassen–Palm wave activity is a well-known example and is central to theoretical analysis. On the mesoscale, while such conservation laws have been worked out in two dimensions, their application to a horizontally homogeneous background flow in three dimensions fails because of a degeneracy created by the absence of a background potential vorticity gradient. Earlier three-dimensional results based on linear WKB theory considered only Doppler-shifted gravity waves, not waves in a stratified shear flow. Consideration of a background flow depending only on altitude is motivated by the parameterization of subgrid-scales in climate models where there is an imposed separation of horizontal length and time scales, but vertical coupling within each column. Here we show how this degeneracy can be overcome and wave-activity conservation laws derived for three-dimensional disturbances to a horizontally homogeneous background flow. Explicit expressions for pseudoenergy and pseudomomentum in the anelastic and Boussinesq models are derived, and it is shown how the previously derived relations for the two-dimensional problem can be treated as a limiting case of the three-dimensional problem. The results also generalize earlier three-dimensional results in that there is no slowly varying WKB-type requirement on the background flow, and the results are extendable to finite amplitude. The relationship between pseudoenergy and pseudomomentum , where c is the horizontal phase speed in the direction of symmetry associated with , has important applications to gravity-wave parameterization and provides a generalized statement of the first Eliassen–Palm theorem.

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J. Vanneste & T. G. Shepherd 1998 On the group-velocity property for wave-activity conservation laws. J. Atmos. Sci. 55, 10631068.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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