A spectral solution of the magneto-convection equations in spherical geometry

A fully three-dimensional solution of the magneto-convection equations—the nonlinearly coupled momentum, induction and temperature equations—is presented in spherical geometry. Two very different methods for solving the momentum equation are presented, corresponding to the limits of slow and rapid rotation, and their relative advantages and disadvantages are discussed. The possibility of including a freely rotating, finitely conducting inner core in the solution of the momentum and induction equations is also discussed.