Thermal Rossby waves in a rotating annulus. Their stability - art. no. 056312

Nonlinear thermal convection in a fast rotating annulus about its axis, wit h slightly inclined ends, radial gravity and heating, is studied numericall y for a fluid of Prandtl number sigma = 0.7 and different values of the rad ius ratio and rotation rate. The properties of the rotating waves that appe ar after the Hopf bifurcation of the conductive slate are analyzed. Near th e 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 Pran dtl number. For different rotation rates, the stability of the primary solu tions as a function of the radius ratio is also studied. The shape of the s tability regions and the type of dominant disturbances that limit these reg ions are very sensitive to the proximity to the value of the radius ratio f or which the type of dominant mode changes.