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Article Type:
Research Article

The Destabilization of Rossby Normal Modes by Meridional Baroclinic Shear

Joseph PedloskyWoods Hole Oceanographic Institution, Woods Hole, Massachusetts

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Print Publication:
01 Aug 2002
DOI:
https://doi.org/10.1175/1520-0485(2002)032<2418:TDORNM>2.0.CO;2
Page(s):
2418–2423
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Abstract

The Rossby normal modes of a two-layer fluid in a meridional channel of width L∗ are altered by the presence of a meridional flow with a small vertical shear. The stability of the modes in the presence of the weak shear is considered. It is found that the joint presence of the Rossby modes and the vertical shear leads to baroclinic instability even for arbitrarily small values of the shear.

The results are used to explain previous numerical calculations of the persistent instability of meridional flows when the ratio βL2D/V > 1, where V is the magnitude of the shear, β is the planetary vorticity gradient, and LD is the deformation radius. If the flow were zonal it would be stable for such weak shears.

The growth rates are weak when βL2D/V ≫ 1 and each unstable mode exists in a narrow range of meridional wavenumber. The asymptotic results qualitatively agree with the earlier numerical results at moderate values of the same parameter.

Corresponding author address: Dr. Joseph Pedlosky, Woods Hole Oceanographic Institution, Clark 363, MS#21, Woods Hole, MA 02543. Email: jpedlosky@whoi.edu

Abstract

The Rossby normal modes of a two-layer fluid in a meridional channel of width L∗ are altered by the presence of a meridional flow with a small vertical shear. The stability of the modes in the presence of the weak shear is considered. It is found that the joint presence of the Rossby modes and the vertical shear leads to baroclinic instability even for arbitrarily small values of the shear.

The results are used to explain previous numerical calculations of the persistent instability of meridional flows when the ratio βL2D/V > 1, where V is the magnitude of the shear, β is the planetary vorticity gradient, and LD is the deformation radius. If the flow were zonal it would be stable for such weak shears.

The growth rates are weak when βL2D/V ≫ 1 and each unstable mode exists in a narrow range of meridional wavenumber. The asymptotic results qualitatively agree with the earlier numerical results at moderate values of the same parameter.

Corresponding author address: Dr. Joseph Pedlosky, Woods Hole Oceanographic Institution, Clark 363, MS#21, Woods Hole, MA 02543. Email: jpedlosky@whoi.edu

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