VISCOUS AND ADIABATIC HEATING EFFECTS IN 3-DIMENSIONAL COMPRESSIBLE CONVECTION AT INFINITE PRANDTL NUMBER

A three-dimensional direct numerical simulation (using a fully spectra l method) of compressible convection of an infinite Prandtl number flu id in a wide box with dimensions 5 x 5 x 1 was conducted. Depth-depend ent viscosity, thermal expansivity, and thermal conductivity have been included in order to model deep-seated processes in the Earth's mantl e. Solutions have been obtained up to a surface Rayleigh number of 4 X 10(7). There is a remarkable contrast between the dynamics of the upp er and lower boundary layers. Very few cylindrical plumes are develope d at the bottom but they merge collectively to form a strong upwelling , which pulses chaotically. Viscous and adiabatic heating are found to become important at high Rayleigh numbers, larger than 10(7). These r esults have important implications on the thermal structure of early E arth, where there might have been dramatic effects from intense mechan ical heating near the top boundary layer.