Convective instability when the temperature gradient and rotation vector are oblique to gravity. I. Fluids without diffusion

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Abstract
We carry out a linear stability analysis of fluid layers under uniform rotation which possess both vertical and horizontal temperature gradients. In order to represent vnrious latitudes with these plane parallel layers we use a rotation vector which is generally oblique to gravity. We consider ideal fiuids without diffusion within a Boussinesq approximation. This simplified configuration is used to assess the preferred convective modes as a function of latitude on a planet like Jupiter. The tilted rotation vector introduces a preference for roll-like disturbanas. with north-south orientations, while the horizontal temperature gradient produces a thermal wind shear which favors convective rolls oriented parallel to the flow in an east-west direction. With both these effects present we find that the horizontal ternperature gradient needed to produce a preference for the axisymmetric or east-west rolls increases with increasing rotation rate and decreasing latitude. The results also indicate that shells with warm-equators have a much stronger preference for east-west rolls than do shells with cold equators. In addition we find that the tilted rotation vector serves to make the symmetric modes unstable even for stable vertical stratifications with Richardson numbers greater than one. We estirnate the pararneter values for Jupiter using a simple radiative-convective rnodel. These values indicate a preference for axisymmetric rolls at virtually a11 latitudes if the convection zone depth is greater than about 200 km below the one atrnosphere pressure level. We fínd that the dynamical characteristics of these convective rolls contribute to an equatorial acceleration. Furthermore, the rnost rapid prograde motions are found at the equatorward edges of the downdrafts, not unlike the zona1 rnotions observed on the planet.