Convection and magnetohydrodynamics in rotating spherical geometry: Simple models and their application to astrophysics

Spherical geometry and rotation are key factors for the study of many geophysical and astrophysical phenomena. In addition, strong temperature gradients develop in planetary and stellar fluid interiors. The Boussinesq approximation is a basic step for understanding flow dynamics in such environments. The formulation and numerical approach to this approximation in the context of thermal convection in rapidly rotating thin shells will be presented together with the main parameters describing the problem. The application to several geophysical (planetary atmospheres or cores) and astrophysical (white dwarfs, neutron stars...) contexts will be outlined.

As an example of simple magnetohydrodynamics problem, the magnetised spherical Couette system will be considered. Some interesting applications to the astrophysical community and advanced experiments of this problem will be commented.