Convection with nonlinear conductivities: feedback effects at low and high Mach number

In the interior of stars like the Sun, convection occurs in the presence of a highly nonlinear radiative conductivity. In this work, we study compressible, stratified convection with a nonlinear radiative conductivity which depends on a Kramer's-like opacity. We show that the Mach number of the resultant convection can be controlled by the opacity's dependence on temperature. In these systems, the Reynolds and Peclet numbers are separately controlled by Rayleigh and Prandtl numbers, so turbulent convection can be studied at low and high Mach number. We determine the importance of nonlinear conductive feedback on the convective flows when the Mach number is low [O(0.01)] and when it is high [O(1)]. We discuss implications for convection in the Sun's deep interior.