Baroclinic Instability of a Rotating Hadley Cell

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  • 1 The University Of Tennessee Space Institute, Tullahoma 37388
  • | 2 Space Sciences Laboratory, Marshall Space Flight Center, Alabama 35812
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Abstract

The stability of a thin fluid layer between two rotating plates which are subjected to a horizontal temperature gradient is studied. First, the solution for the stationary basic state is obtained in a closed form. This solution identifies Ekman and thermal layers adjacent to the plates and interior temperature and velocity fields which are almost linear functions of height. Then the stability of that basic state with respect to infinitesimal zonal waves is analyzed via the solution of the complete viscous linear equations for the perturbations. The character of the growth rates is found to be similar to the growth rates of the classical baroclinic waves. The neutral stability curves for these waves possessed a knee in the Rossby-Taylor number plane to the left of which all perturbations are stable. The region of instability is found to depend on the Prandtl number, the vertical stratification parameter, and both the meridional and zonal wavenumbers. It is found in general that the flow is unstable for small enough Ekman numbers and for Rossby numbers less than 10. It is also found that increased vertical stable stratification and increased Prandtl number stabilize the flow.

Abstract

The stability of a thin fluid layer between two rotating plates which are subjected to a horizontal temperature gradient is studied. First, the solution for the stationary basic state is obtained in a closed form. This solution identifies Ekman and thermal layers adjacent to the plates and interior temperature and velocity fields which are almost linear functions of height. Then the stability of that basic state with respect to infinitesimal zonal waves is analyzed via the solution of the complete viscous linear equations for the perturbations. The character of the growth rates is found to be similar to the growth rates of the classical baroclinic waves. The neutral stability curves for these waves possessed a knee in the Rossby-Taylor number plane to the left of which all perturbations are stable. The region of instability is found to depend on the Prandtl number, the vertical stratification parameter, and both the meridional and zonal wavenumbers. It is found in general that the flow is unstable for small enough Ekman numbers and for Rossby numbers less than 10. It is also found that increased vertical stable stratification and increased Prandtl number stabilize the flow.

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