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Baroclinic Instability of Two-Layer Flows over One-Dimensional Bottom Topography

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  • 1 Department of Mathematics, University of Limerick, Limerick, Ireland
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Abstract

Using the QG approximation, the stability of two-layer zonal flows on the beta plane over bottom topography is examined. The topography is assumed to be one-dimensional, with the isobaths being directed at a fixed angle to the streamlines of the flow. The horizontal spatial scale of bottom irregularities is assumed to be much shorter than the deformation radius. The dispersion relation for the growth rate of baroclinic instability is determined, the analysis of which demonstrated the following:

1) The effect of topography is the strongest when the isobaths are parallel to the wavevector of the disturbance. If the isobaths are perpendicular to the wavevector, the topography does not affect the disturbance at all.

2) Topography weakens baroclinic instability and shifts the range of unstable disturbances toward the short-wave end of the spectrum.

3) The effect of bottom topography on flows localized in a thin upper layer is relatively weak. Flows with a “thick” active layer are affected to a greater extent: for the Antarctic Circumpolar Current, for example, bottom irregularities of mean height 200 m may diminish the growth rate of baroclinic instability by a factor of 4.

Corresponding author address: E. S. Benilov, Dept. of Mathematics, University of Limerick, Limerick, Ireland. Email: eugene.benilov@ul.ie

Abstract

Using the QG approximation, the stability of two-layer zonal flows on the beta plane over bottom topography is examined. The topography is assumed to be one-dimensional, with the isobaths being directed at a fixed angle to the streamlines of the flow. The horizontal spatial scale of bottom irregularities is assumed to be much shorter than the deformation radius. The dispersion relation for the growth rate of baroclinic instability is determined, the analysis of which demonstrated the following:

1) The effect of topography is the strongest when the isobaths are parallel to the wavevector of the disturbance. If the isobaths are perpendicular to the wavevector, the topography does not affect the disturbance at all.

2) Topography weakens baroclinic instability and shifts the range of unstable disturbances toward the short-wave end of the spectrum.

3) The effect of bottom topography on flows localized in a thin upper layer is relatively weak. Flows with a “thick” active layer are affected to a greater extent: for the Antarctic Circumpolar Current, for example, bottom irregularities of mean height 200 m may diminish the growth rate of baroclinic instability by a factor of 4.

Corresponding author address: E. S. Benilov, Dept. of Mathematics, University of Limerick, Limerick, Ireland. Email: eugene.benilov@ul.ie

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