Thermal Rossby waves in a rotating annulus. Their stability.

Nonlinear thermal convection in a fast rotating annulus about its axis, with slightly inclined ends, radial gravity and heating, is studied numerically for a fluid of Prandtl number sigma=0.7 and different values of the radius ratio and rotation rate. The properties of the rotating waves that appear after the Hopf bifurcation of the conductive state are analyzed. Near the critical Rayleigh number, different types of solutions with the same wave number coexist, and they are classified as a function of their connection with the two types of modes identified in the linear analysis for this Prandtl number. For different rotation rates, the stability of the primary solutions as a function of the radius ratio is also studied. The shape of the stability regions and the type of dominant disturbances that limit these regions are very sensitive to the proximity to the value of the radius ratio for which the type of dominant mode changes.