NONLINEAR COMPRESSIBLE CONVECTION IN OBLIQUE MAGNETIC-FIELDS

Magnetoconvection in the Sun does not take place in the idealized situ ation in which the imposed field is vertical or horizontal. Instead, f ields in sunspots and other active region features are inclined to the vertical, and so the system does not possess the left-right symmetry that is a feature of many analytical and numerical studies. As a first step toward the understanding of convection in general field configur ations, we consider the nonlinear behavior of compressible convection in the presence of a uniform, externally imposed, oblique magnetic hel d. Numerical simulations demonstrate that all solutions take the form of traveling waves, regardless of the degree of nonlinearity or field intensity, for angles of obliquity 0 < phi < pi/2. However, the struct ure of the convection cells, their wave speed, and direction depend se nsitively upon the degree of nonlinearity, field angle, and field stre ngth. For sufficiently vigorous convection, we find that all solutions have a net horizontal velocity at the upper surface of the computatio nal domain that is in the direction of the field tilt from vertical (w hereas the total horizontal momentum is zero). In cases where the conv ection dominates over the magnetic field, we find the waves propagatin g in the same direction as the net surface velocity but with phase vel ocities that are typically an order of magnitude smaller. In cases whe re the field dominates over the convection, we find a similar relation in speeds but with waves propagating in the opposite direction. The r esults appear to be qualitatively independent of the precise boundary conditions applied to the field, as long as the latter do not impart a net horizontal momentum to the layer.