Planetary Waves in Horizontal and Vertical Shear: The Generalized Eliassen-Palm Relation and the Mean Zonal Acceleration

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  • 1 U.K. Universities’ Atmospheric Modelling Group, Department of Geophysics, University of Reading, and Department of Applied Mathematics and Theoretical Physics, University of Cambridge
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Abstract

Using a new generalization of the Eliassen-Palm relations, we discuss the zonal-mean-flow tendency ∂ū/∂t due to waves in a stratified, rotating atmosphere, with particular attention to equatorially trapped modes. Wave transience, forcing and dissipation are taken into account in a very general way. The theory makes it possible to discuss the latitudinal (y) and vertical (z) dependence of ∂ū/∂t qualitatively and calculate it directly from an approximate knowledge of the wave structure. For equatorial modes it reveals that the y profile of ∂ū/∂t is strongly dependent on the nature of the forcing or dissipation mechanism. A by-product of the theory is a far-reaching generalization of the theorems of Charney-Drazin, Dickinson and Holton on the forcing of ∂ū/∂t by conservative linear waves.

Implications for the quasi-biennial oscillation in the equatorial stratosphere are discussed. Graphs of y profiles of ∂ū/∂t are given for the equatorial waves considered in the recent analysis of observational data by Lindzen and Tsay (1975). The y profile of ∂ū/∂t for Rossby-gravity and inertio-gravity modes, in Lindzen and Tsay's parameter ranges, prove extremely sensitive to whether or not small amounts of mechanical dissipation are present alongside the radiative-photochemical dissipation of the waves.

The probable importance of low-frequency Rossby waves for the momentum budget of the descending easterlies is suggested.

Abstract

Using a new generalization of the Eliassen-Palm relations, we discuss the zonal-mean-flow tendency ∂ū/∂t due to waves in a stratified, rotating atmosphere, with particular attention to equatorially trapped modes. Wave transience, forcing and dissipation are taken into account in a very general way. The theory makes it possible to discuss the latitudinal (y) and vertical (z) dependence of ∂ū/∂t qualitatively and calculate it directly from an approximate knowledge of the wave structure. For equatorial modes it reveals that the y profile of ∂ū/∂t is strongly dependent on the nature of the forcing or dissipation mechanism. A by-product of the theory is a far-reaching generalization of the theorems of Charney-Drazin, Dickinson and Holton on the forcing of ∂ū/∂t by conservative linear waves.

Implications for the quasi-biennial oscillation in the equatorial stratosphere are discussed. Graphs of y profiles of ∂ū/∂t are given for the equatorial waves considered in the recent analysis of observational data by Lindzen and Tsay (1975). The y profile of ∂ū/∂t for Rossby-gravity and inertio-gravity modes, in Lindzen and Tsay's parameter ranges, prove extremely sensitive to whether or not small amounts of mechanical dissipation are present alongside the radiative-photochemical dissipation of the waves.

The probable importance of low-frequency Rossby waves for the momentum budget of the descending easterlies is suggested.

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