MAGNETOCONVECTION DYNAMICS IN A STRATIFIED LAYER .1. 2-DIMENSIONAL SIMULATIONS AND VISUALIZATION

To gain insight in the problem of fluid convection below the solar pho tosphere, time-dependent magnetohydrodynamic convection is studied by numerical simulation of the magneto-anelastic equations, a model appro priate for low Mach numbers. Numerical solutions to the equations are generated on a two-dimensional Cartesian mesh by a finite-difference, predictor-corrector algorithm. The thermodynamic properties of the flu id are held constant at the rigid, stress-free top and bottom boundari es of the computational box, while lateral boundaries are treated as p eriodic. In most runs the background polytropic fluid configuration is held fixed at Rayleigh number R = 5.44 times the critical value, Pran dtl number P = 1.8, and aspect ratio a = 1, while the magnetic paramet ers are allowed to vary. The resulting dynamical behavior is shown to be strongly influenced by a horizontal magnetic field which is imposed at the bottom boundary. As the field strength increases from zero, an initially unsteady ''single-roll'' state, featuring complex time depe ndence, is replaced by a steady ''traveling-wave'' tilted state; then, an oscillatory or ''sloshing'' state; then, a steady two-roll state w ith no tilting; and finally, a stationary state. Because the magnetic field is matched onto a potential field at the top boundary, it can pe netrate into the nonconducting region above. By varying the magnetic d iffusivity, the concentrations of weak magnetic fields at the top of t hese flows can be shown to be explainable in terms of an advection-dif fusion balance.