Theory of nonlinear magnetoconvection and its application to solar convection problems. I, II

Abstract

Two- and three-dimensional nonlinear direct and oscillatory magnetoconvection (MC) in a Boussinesq fluid in the presence of an imposed vertical magnetic field is studied analytically with the object of understanding solar convection problems. It is shown that oscillatory (overstable) motions occur for a restricted range (B < 1) of the ratio of magnetic to thermal diffusivities B and the Chandrasekhar number Q, because thereby the stabilizing effect of the Lorentz force can be reduced. The sequence of preferred finite amplitude motions is discussed in detail. The values of heat transport for rolls differ markedly from those of limiting rectangles (LR) and the values of Q at which the preferred cell pattern crosses over from rolls to LR depend upon the values of B. The convective heat transport for fixed Q and variable Rayleigh number and vice versa is computed. It is shown that for Q<lO^-2 (kinematic regime) the heat transport is by steady rolls, whereas for Q ≥ 1 (dynamic regime) it is by overstable motions. It is also shown that the change in the frequency has marked effect on the heat transport. Quantitative results are given in several tables and diagrams.