Abstract

Motivated by astrophysical-geophysical applications, we have performed a series of high Reynolds number simulations of magnetohydrodynamic shallow-water turbulence (MHDSWT) on a rotating sphere. MHDSWT is the simplest turbulence model that allows the effects of differential rotation, stratification and magnetic field to be studied over long simulation times. A systematic exploration of the full physical and numerical parameter-space shows novel as well as consistent behavior, compared with those of pure hydrodynamic (HD) and 2-D MHD counterparts. In the case without rotation and weak magnetic field strength, the turbulent evolution is sensitive to initial conditions, with the strongest dependence on the peak of the initial energy spectrum. With increasing magnetic field strength, the flow field is more susceptible to loss of balance, and the field blows up in finite time. In addition, the pronounced zonal structures observed in differentially-rotating HD systems do not form.