A NUMERICAL-SIMULATION OF SUPERSONIC THERMAL-CONVECTION

A computational scheme has been constructed for solving the equations that describe strong thermal convection in a two-dimensional gas layer that is heated from below and is stratified across many scaleheights by a uniform gravitational field. The purpose of this schemes to mimic the physical conditions that may have existed in a section of the pro to-solar cloud from which the planetary system formed. The vertical te mperature gradient of the initial quiescent layer of diatomic gas is s trongly superadiabatic and matches that of a polytrope of index m = 1. The temperature at the upper boundary is kept fixed during the comput ation. Because of the highly compressible nature of the gas and the st eep spatial gradients, a modified version of a flux-corrected transpor t scheme due to Zalesak is devised. The computations show that after t he convection adopts a steady-state configuration, the flow consists o f horizontal pairs of giant convective cells of opposing circulation. At the cell boundaries, the downflows are rapid and spatially concentr ated while the upflows are broad and sluggish. Supersonic speeds are e asily achieved in the downflows. Contrary to the expectations of the m ixing length theory of convection, there is a net downward flux of kin etic energy at each level in the layer. The convecting layer is cooler on average compared with the initial temperature profile, and there i s a net shift of mass towards the lower boundary. The implications of these results for the modern Laplacian theory of Solar system origin a re briefly discussed.