Convective instability when the temperature gradient and rotation vector are oblique to gravity. II. Real fluids with effects of diffusion

Abstract

The linear stability analysis of Hathaway, Gilman and Toomre (1979) (hereafter referred to as Paper I) is repeated for Boussinesq fluids with viscous and thermal diffusion. As in Paper I the fluid is confined between plane parallel boundaries and the rotation vector is oblique to gravity. This tilted rotation vector introduces a preference for roll-like disturbances whose axes are oriented north-south; the preference is particularly strong in the equatorial region. The presence of a latitudinal temperature gradient produces a thermal wind shear which favors axisymmetric convective rolls if the gradient exceeds some critical value. For vanishingly small diffusivities the value of this transition temperature gradient approaches the inviscid value found in Paper I. For larger diffusivities larger gradients are required particularly in the high latitudes. These results are largely independent of the Prandtl number. Diffusion tends to stabilize the large wavenumber rolls with the result that a unique wavenumber can be found at which the growth rate is maximized. These preferred rolls have widths comparable to the depth of the layer and tend to be broader near the equator. The axisymmetric rolls are similar in many respects to the cloud bands on Jupiter provided they extend to a depth of about 15,000 km.