Viscous and adiabatic heating effects in three-dimensional compressible convection at infinite Prandtl number

A three-dimensional direct numerical simulation (using a fully spectral method) of compressible convection of an infinite Prandtl number fluid in a wide box with dimensions 5×5×1 was conducted. Depth-dependent viscosity, thermal expansivity, and thermal conductivity have been included in order to model deep-seated processes in the Earth's mantle. Solutions have been obtained up to a surface Rayleigh number of 4×10⁷. There is a remarkable contrast between the dynamics of the upper and lower boundary layers. Very few cylindrical plumes are developed 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 results have important implications on the thermal structure of early Earth, where there might have been dramatic effects from intense mechanical heating near the top boundary layer.