Numerical investigation of atmospherelike flows in a spherical geometry

Buoyancy-driven convection flows play a crucial role in global heat and momentum transport in atmosphere. Simplified planetary and stellar atmospheres can be described by a spherical gap geometry with special boundary conditions for the temperature. In the spherical gap, the dielectrophoretic effect is used to synthesize the radial gravity field. Lateral thermal boundary conditions are used to model solar radiation at the equator and at the poles. The temperature reaches a maximum value at the equator and becomes colder near the poles. In the case of a rotating gap, the influence of the Coriolis and centrifugal forces are taken into account. Different regimes of the two-dimensional steady basic flow are discussed in dependence on the Taylor number and Rayleigh number and for the radii ratio η=R_{in}/R_{out}, where R_{in},R_{out} are the radii of the inner and outer surfaces, respectively. Linear instability theory is used to study when the basic flow becomes unstable. The critical Rayleigh number at which the steady axisymmetric basic flow becomes time-dependently axisymmetric or three dimensional is found to be a function of the Taylor number. Furthermore, the critical azimuthal wave number m_{c}, which is responsible for the structure of the supercritical three-dimensional flow, and the critical frequency of the perturbation ω_{c} were found. The spatial location of the perturbation helps to understand the origin of the instability.