Non-Boussinesq convection at low Prandtl numbers relevant to the Sun

Convection in the Sun occurs at Rayleigh numbers, , as high as and molecular Prandtl numbers, , as low as , under conditions that are far from satisfying the Oberbeck-Boussinesq (OB) idealization. The effects of these extreme circumstances on turbulent heat transport are unknown, and no comparable conditions exist on Earth. Our goal is to understand how these effects scale (since we cannot yet replicate the Sun's conditions faithfully). We study thermal convection by using direct numerical simulations, and determine the variation with respect to , to values as low as , of the turbulent Prandtl number, , which is the ratio of turbulent viscosity to thermal diffusivity. The simulations are primarily two-dimensional but we draw upon some three-dimensional results as well. We focus on non-Oberbeck-Boussinesq (NOB) conditions of a certain type, but also study OB convection for comparison. The OB simulations are performed in a rectangular box of aspect ratio 2 by varying from to at fixed Grashof number . The NOB simulations are done in the same box by letting only the thermal diffusivity depend on the temperature. Here, the Rayleigh number is fixed at the top boundary while the mean varies in the bulk from 0.07 to . The three-dimensional simulations are performed in a box of aspect ratio 25 at a fixed Rayleigh number of , and . The principal finding is that increases with decreasing in both OB and NOB convection: for OB convection and for the NOB case. The dependence for the NOB case especially suggests that convective flows in the astrophysical settings behave effectively as in high-Prandtl-number turbulence.