Metamorphosis of marginal thermal convection in rapidly rotating selfgravitating spherical shells
Abstract
Thermal convection in rapidly rotating systems is investigated numerically with selfgravitating spherical shells, within Boussinesq approximation, with the radius of the inner sphere eta = 0.4 relative to that of the outer sphere. Marginal convection experiences a series of metamorphoses with decreasing Prandtl number: from the columnar mode to the spiralling mode, and then to the wallattached mode. The physical processes of the metamorphoses are clarified by diagnosing both the vorticity and the thermodynamic balances. At the limit of high Prandtl number, marginal convection overcomes the TaylorProudman constraint by forming an internal kinematic viscous boundary layer: the marginal mode takes a form of columnar Taylor convection columns confined to a narrow cylindrical shell. The active invocation of the kinematic diffusivity has the advantage of keeping the convection columns as stationary as possible. However, with decrease of the Prandtl number, the viscosity becomes less effective in maintaining the steadiness: the fluid parcel is accelerated strongly in the radial direction by the buoyancy force without balancing with kinematic diffusivity. As a consequence, the convection columns are twisted into a spiralling pattern. Within this spiralling pattern a thermal diffusive boundary layer is formed: the thermal diffusivity in turn plays a role in maintaining the steadiness of the motion as much as possible in the phase of this spiralling mode. The main difference between the viscousboundary layer driven columnar mode and the thermaldiffusively driven spiralling mode is that in the former the kinematic diffusion does help to initiate convection, while the latter requires a higher critical temperature gradient to initiate convection by overcoming thermal diffusivity. For this reason, the spiralling mode is an increasingly less preferable morphology for convection on further decrease of the Prandtl number, and eventually transits into the wallattached mode, which is described as an inertial oscillation without any effective contribution of diffusivities to the dynamics.
 Publication:

Geophysical and Astrophysical Fluid Dynamics
 Pub Date:
 March 1994
 DOI:
 10.1080/03091929408203637
 Bibcode:
 1994GApFD..74..143H
 Keywords:

 Convective Heat Transfer;
 Free Convection;
 Prandtl Number;
 Spherical Shells;
 Thermal Boundary Layer;
 Thermal Diffusivity;
 Vorticity;
 Boundary Layer Flow;
 Mathematical Models;
 Morphology;
 Oscillations;
 Temperature Gradients