A formulation of a wave-activity flux for stationary Rossby waves on a zonally varying basic flow
Abstract
A new formulation of an approximate conservation relation is proposed for stationary Rossby waves on a zonally varying basic flow, utilizing that A (proportional to wave enstrophy) and ɛ (proportional to wave energy) are both related to the wave activity pseudomomentum. For stationary Rossby waves, it is shown in the limit of a small-amplitude, plane wave on a slowly varying, unforced non-zonal flow that a particular linear combination of A and ɛ, namely, M ≡ (A + ɛ)/2, is independent of the wave phase, even if unaveraged, and is conserved under steady, unforced and nondissipative conditions. It is also shown that the three-dimensional flux of M is parallel to the local group velocity in the WKB limit. The flux could be a useful diagnostic tool, as shown in an example that presents a “snapshot” of the three-dimensional propagation of a stationary Rossby wavetrain in the real atmosphere. Our conservation relation is a generalization of that for stationary Rossby waves on a zonally-uniform basic flow derived by Plumb.
- Publication:
-
Geophysical Research Letters
- Pub Date:
- December 1997
- DOI:
- 10.1029/97GL03094
- Bibcode:
- 1997GeoRL..24.2985T
- Keywords:
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- Meteorology and Atmospheric Dynamics: General circulation;
- Meteorology and Atmospheric Dynamics: Waves and tides