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 bo ttom boundaries, radial gravity, and internal heating is numerically analyz ed. It is shown that for moderate and high Prandtl numbers, the onset of co nvection is described by a competition of azimuthal thermal modes with diff erent radial structure, which dominate in different regions of the paramete r space. By the combined effect of the inclined ends and rotation, there ar e modes that are attached to the heated wall and slanted to the prograde di rection of rotation, and others which are straight and fill the convective layer. Nevertheless, for very small Prandtl numbers the velocity field of t he dominant modes corresponds essentially to the inertial solution of the P oincare equation, and the temperature perturbation is forced by this veloci ty field. In addition, a detailed exploration of the critical Rayleigh numb ers and precession frequencies of the convective modes versus the radius ra tio and the Coriolis parameter, for different Prandtl numbers, is presented .