A quasi-geostrophic convection model for planetary systems using a domain decomposition method

A numerical study is described of a quasi-geostrophic model for thermal convection in rapidly rotating planetary systems where the effect of Coriolis forces is dynamically predominant. In the quasi-geostrophic convection model, a spherical shell is divided into the three domains: a spherical annulus outside the tangent cylinder touching the equator of the inner sphere, the southern and northern polar regions inside the tangent cylinder. Convection in the rotating spherical annulus is investigated using a quasi-two-dimensional geostrophic approximation. Both linear stability analysis and fully nonlinear simulations are carried out. A new domain decomposition method suitable for massively parallel computers is employed in numerical simulations. It is found that, while the structure of mildly nonlinear flows at R=O(10Rc), where R denotes the Rayleigh number and Rc is its critical value at the onset of convection, is spatially complicated and irregular, the structure of strongly nonlinear flows at R=O(100Rc) is dominated by an axisymmetric zonal flow that is largely laminar, stable and nearly time-independent, similar to that on giant planets Jupiter and Saturn. We also model the atmospheric circulation of a 51 Pegasus b-type extrasolar planet which is synchronized with its parent star and receives an intensive radiation on its dayside.