Rotating Magnetoconvection with Magnetostrophic Balance

The linear theory for the onset of convection in a rotating layer with an imposed vertical magnetic field is studied for large Taylor (Ta) and Chandrasekhar (Q) numbers. The velocity and magnetic field perturbations are in magnetostrophic balance. For small values of σ = ν/κ and ζ = η/κ, where ν, κ and η are the kinematic viscosity, and thermal and ohmic diffusivities, three oscillatory modes are typically present, and these undergo a complex sequence of transitions as parameters are varied. Two of these modes are related to the MAC (Magneto-ArchimedeanCoriolis) modes discussed by Braginskii, while the third is a magnetoconvective mode. Three different asymptotic regimes are identified in the limit of large Ta and Q, depending on their relative magnitude, and the characteristics of the three modes in each regime are described in detail. Of greatest interest is the regime Ta = O(Q 3 2 ) which captures all the transitions among the three modes including the transition to steady convection.