On large-scale solar convection

We examine the effects of rotation about a vertical axis on thermal convection with a simple model in which an inviscid, incompressible fluid of zero thermal conductivity and electrical resistivity is contained in a thin annulus of rectangular cross-section. The initial steady state assumed is one of no motion relative to the rotating frame with constant (unstable) vertical temperature gradient and uniform toroidal magnetic field. Small periodic disturbances are then introduced and the linearized perturbation equations solved. We also determine the second-order mean circulations and magnetic fields that are forced by non-zero Reynolds and thermal stresses and magnetic field transports. The solutions have several properties which are relevant to large-scale solar phenomena if giant long-lived convection cells exist on the sun. In particular, the convective cells are tilted in latitude in the same sense as bipolar magnetic regions, and induce vertical magnetic fields with the same tilt. They transport momentum across latitude circles through Reynolds stresses and induced meridional circulations thus setting up a differential rotation. Cells which grow slowly compared to the rotation rate and have comparable dimensions in latitude and longitude transport momentum toward the equator. The cells also form a poloidal magnetic field from initial toroidal field, in a manner similar to that put forth by Parker.