NONLINEAR COMPRESSIBLE MAGNETOCONVECTION .3. TRAVELING WAVES IN A HORIZONTAL FIELD

We present results of numerical experiments on two-dimensional compres sible convection in a polytropic layer with an imposed horizontal magn etic field. Our aim is to determine how far this geometry favours the occurrence of travelling waves. We therefore delineate the region of p arameter space where travelling waves are stable, explore the ways in which they lose stability and investigate the physical mechanisms that are involved. In the magnetically dominated regime (with the plasma b eta, beta = 8), convection sets in at an oscillatory bifurcation and t ravelling waves are preferred to standing waves. Standing waves are st able in the strong-field regime (beta = 32) but travelling waves are a gain preferred in the intermediate region (beta = 128), as suggested b y weakly nonlinear Boussinesq results. In the weak-field regime (beta greater than or equal to 512) the steady nonlinear solution undergoes symmetry-breaking bifurcations that lead to travelling waves and to pu lsating waves as the Rayleigh number, ($) over cap R, is increased. Th e numerical experiments are interpreted by reference to the bifurcatio n structure in the (beta, ($) over cap R)-plane, which is dominated by the presence of two multiple (Takens-Bogdanov) bifurcations. Physical ly, the travelling waves correspond to slow magnetoacoustic modes, whi ch travel along the magnetic field and are convectively excited. We co nclude that they are indeed more prevalent when the held is horizontal than when it is vertical.