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

A linear stability analysis of fluid layers under uniform rotation (generally oblique to gravity) which possess both vertical and horizontal temperature gradients is made by considering ideal fluids 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 disturbances 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. It is found that the horizontal temperature gradient needed to produce a preference for the axisymmetric or east-west rolls increases with an increasing rotation rate and a decreasing latitude. The parameter values for Jupiter are estimated with the use of a simple radiative convective model, indicating a preference for axisymmetric rolls at nearly all latitudes if the convection zone depth is greater than about 200 km below the one atmosphere pressure level and convective roll characteristics which contribute to an equatorial acceleration.