MAGNETOCONVECTION DYNAMICS IN A STRATIFIED LAYER .2. A LOW-ORDER MODEL OF THE TILTING INSTABILITY

Simulations of nonlinear, anelastic convection in the presence of magn etic fields have revealed a complex array of dynamic phenomena, includ ing several kinds of nonlinear oscillations (Lantz & Sudan 1995). In a n attempt to identify the physical mechanism responsible for these osc illations, a simple model is proposed in which the full magneto-anelas tic equations are replaced by equations for the amplitudes of only a f ew Fourier modes, which evolve according to more symmetric Boussinesq rules. Only one symmetry is permitted to be broken: the up-down mirror symmetry, via a tilting mode that drives a shear flow in the horizont al direction (Howard & Krishnamurti 1986). The nonlinear interaction o f just these few modes is shown to be adequate to reproduce qualitativ ely the kinds of behaviors seen in simulations. Furthermore, when para meters in the magneto-anelastic equations are mapped onto rough Boussi nesq equivalents, a number of quantitative comparisons can be made as well; these confirm that the low-order, truncated model is able to cap ture the correct numerical trends in the simulation data as the Raylei gh number and the imposed horizontal magnetic held are varied. Video v isualizations of fluid motions derived from the low-order equations ar e presented, together with their analogs from full MHD simulations.