The Double-Diffusive Modes of Symmetric Instability on an Equatorial Beta-Plane

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  • 1 National Center for Atmospheric Research, Boulder, CO 80307
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Abstract

The symmetric instability due to horizontal shear on an equatorial beta-plane exhibits two distinct modes of instability. The classical monotonic non-oscillatory instability exists for all Prandtl numbers but is favored when the Prandtl number is approximately less than 3/2. For values of Prandtl number approximately larger than this we find that an oscillating “overstability” is the preferred mode of instability. This result contrasts with the baroclinic centrifugally stable case in which overstabilities exist but are never preferred. Similar results can be demonstrated analytically on an artificially bounded f-plane which mimics the finite latitudinal scale imposed by the equatorial beta-plane geometry. Radiative relaxation would favor the monotonic mode, but the effect might be insignificant if breaking internal gravity waves are present.

Abstract

The symmetric instability due to horizontal shear on an equatorial beta-plane exhibits two distinct modes of instability. The classical monotonic non-oscillatory instability exists for all Prandtl numbers but is favored when the Prandtl number is approximately less than 3/2. For values of Prandtl number approximately larger than this we find that an oscillating “overstability” is the preferred mode of instability. This result contrasts with the baroclinic centrifugally stable case in which overstabilities exist but are never preferred. Similar results can be demonstrated analytically on an artificially bounded f-plane which mimics the finite latitudinal scale imposed by the equatorial beta-plane geometry. Radiative relaxation would favor the monotonic mode, but the effect might be insignificant if breaking internal gravity waves are present.

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