Magnetoconvection Dynamics in a Stratified Layer. II. A Low-Order Model of the Tilting Instability

Simulations of nonlinear, anelastic convection in the presence of magnetic fields have revealed a complex array of dynamic phenomena, including several kinds of nonlinear oscillations (Lantz & Sudan 1993). In an attempt to identify the physical mechanism responsible for these oscillations, a simple model is proposed in which the full magnetoanelastic equations are replaced by equations for the amplitudes of only a few 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 horizontal direction (Howard & Krishnamurti 1986). The nonlinear interaction of just these few modes is shown to be adequate to reproduce qualitatively the kinds of behaviors seen in simulations. Furthermore, when parameters in the magneto-anelastic equations are mapped onto rough Boussinesq equivalents, a number of quantitative comparisons can be made as well; these confirm that the low-order, truncated model is able to capture the correct numerical trends in the simulation data as the Rayleigh number and the imposed horizontal magnetic field are varied. Video visualizations of fluid motions derived from the low-order equations are presented, together with their analogs from full MHD simulations. 2 -