Eigenfrequencies and Horizontal Structure of Divergent Barotropic Instability Originating in Tropical Latitudes

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  • 1 Northwest Research Associates, Inc., Bellevue, Washington
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Abstract

Instabilities arising on a latitudinally sheared mean flow fall into one of at least two classes: inertial instabilities associated with a reversed potential vorticity and barotropic instabilities associated with a reversed meridional gradient of potential vorticity. Both types of instability are described by the generalized Laplace tidal equation, a horizontal structure equation that explicitly includes the effect of horizontal divergence on the disturbances. The effect of horizontal divergence on barotropic instability has not been extensively studied. A systematic investigation of the eigenfunctions of the generalized Laplace tidal equation for monotonic mean zonal wind profiles having a single, narrow region of reversed vorticity gradient in tropical latitudes reveals that, in the limit of low planetary zonal wavenumber, the modes of barotropic instability bifurcate into weakly divergent modes of hemispheric scale, and strongly divergent, “internal” modes trapped about the source region, i.e., equatorially trapped. Disturbances in the second category penetrate into the deep tropics—the side of the critical latitude with positive intrinsic frequency—as a Kelvin wave type of behavior not previously seen in this context.

These results suggest, first, that hemispheric barotropic instability need not be purely nondivergent. In fact, the growth of weakly divergent modes is preferred. Their equivalent depth is similar to that of free neutral modes of the homogeneous vertical structure equation. Second, the existence of equatorially trapped divergent barotropic instability may be of interest in the tropical troposphere and mesosphere. The equatorial amplitude of these disturbances can be significant, and their frequency, which is generally less than that of a dry Kelvin wave, is determined by a critical latitude in the region of reversed vorticity gradient.

Abstract

Instabilities arising on a latitudinally sheared mean flow fall into one of at least two classes: inertial instabilities associated with a reversed potential vorticity and barotropic instabilities associated with a reversed meridional gradient of potential vorticity. Both types of instability are described by the generalized Laplace tidal equation, a horizontal structure equation that explicitly includes the effect of horizontal divergence on the disturbances. The effect of horizontal divergence on barotropic instability has not been extensively studied. A systematic investigation of the eigenfunctions of the generalized Laplace tidal equation for monotonic mean zonal wind profiles having a single, narrow region of reversed vorticity gradient in tropical latitudes reveals that, in the limit of low planetary zonal wavenumber, the modes of barotropic instability bifurcate into weakly divergent modes of hemispheric scale, and strongly divergent, “internal” modes trapped about the source region, i.e., equatorially trapped. Disturbances in the second category penetrate into the deep tropics—the side of the critical latitude with positive intrinsic frequency—as a Kelvin wave type of behavior not previously seen in this context.

These results suggest, first, that hemispheric barotropic instability need not be purely nondivergent. In fact, the growth of weakly divergent modes is preferred. Their equivalent depth is similar to that of free neutral modes of the homogeneous vertical structure equation. Second, the existence of equatorially trapped divergent barotropic instability may be of interest in the tropical troposphere and mesosphere. The equatorial amplitude of these disturbances can be significant, and their frequency, which is generally less than that of a dry Kelvin wave, is determined by a critical latitude in the region of reversed vorticity gradient.

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