Viscous Nongeostrophic Baroclinic Instability

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  • 1 Systems Dynamics Laboratory, Marshall Space Flight Center, Huntsville, AL 35812
  • | 2 Space Science Laboratory, Marshall Space Flight Center, Huntsville, AL 35812
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Abstract

Calculations have been performed of the (linear) stability of a baroclinic flow to three-dimensional perturbations. Both the simple Eady basic state and the rotating Hadley cell of Antar and Fowlis are considered. The independent influences of the Richardson (Ri), thermal Rossby (baroclinicity), Ekman, and Prandtl numbers are examined, as well as the influences of the angle of orientation of the horizontal wave vector and the wavelength.

It is shown that if the wavelength is allowed to vary freely, disturbances of the Eady type are preferred (i.e., have greatest growth rate) unless Ri and Ekman numbers are small enough and the thermal Rossby number is large enough. In the latter case, disturbances whose angles of orientation are almost symmetric and whose wavelengths are mesoscale are preferred. If, on the other hand, the wavelength is fixed at a mesoscale size, only the symmetric and almost symmetric modes have growth. By allowing the wave vector orientation to deviate from purely symmetric, we note that the region of instability (i.e., critical Ri) is increased, the extent of which is greater for longer wavelength. For Prandtl number = 1, permitting the angle to be nonsymmetric demonstrates the existence of two maxima in growth rate at opposite angles of orientation and with very different energetics. For Prandtl number far enough from one and for large enough dissipation, only one of these two modes has positive growth rates. Growing oscillatory modes were found for some cases.

Abstract

Calculations have been performed of the (linear) stability of a baroclinic flow to three-dimensional perturbations. Both the simple Eady basic state and the rotating Hadley cell of Antar and Fowlis are considered. The independent influences of the Richardson (Ri), thermal Rossby (baroclinicity), Ekman, and Prandtl numbers are examined, as well as the influences of the angle of orientation of the horizontal wave vector and the wavelength.

It is shown that if the wavelength is allowed to vary freely, disturbances of the Eady type are preferred (i.e., have greatest growth rate) unless Ri and Ekman numbers are small enough and the thermal Rossby number is large enough. In the latter case, disturbances whose angles of orientation are almost symmetric and whose wavelengths are mesoscale are preferred. If, on the other hand, the wavelength is fixed at a mesoscale size, only the symmetric and almost symmetric modes have growth. By allowing the wave vector orientation to deviate from purely symmetric, we note that the region of instability (i.e., critical Ri) is increased, the extent of which is greater for longer wavelength. For Prandtl number = 1, permitting the angle to be nonsymmetric demonstrates the existence of two maxima in growth rate at opposite angles of orientation and with very different energetics. For Prandtl number far enough from one and for large enough dissipation, only one of these two modes has positive growth rates. Growing oscillatory modes were found for some cases.

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