Thermal and inertial modes of convection in a rapidly rotating annulus.

The nature of the primary instabilities that arise in a fluid contained in a fast rotating cylindrical annulus with slightly inclined plane top and bottom boundaries, radial gravity, and internal heating is numerically analyzed. It is shown that for moderate and high Prandtl numbers, the onset of convection is described by a competition of azimuthal thermal modes with different radial structure, which dominate in different regions of the parameter space. By the combined effect of the inclined ends and rotation, there are modes that are attached to the heated wall and slanted to the prograde direction of rotation, and others which are straight and fill the convective layer. Nevertheless, for very small Prandtl numbers the velocity field of the dominant modes corresponds essentially to the inertial solution of the Poincare equation, and the temperature perturbation is forced by this velocity field. In addition, a detailed exploration of the critical Rayleigh numbers and precession frequencies of the convective modes versus the radius ratio and the Coriolis parameter, for different Prandtl numbers, is presented.