Simulations of two-dimensional turbulent convection in a density-stratified fluid

High resolution computer simulations of two-dimensional convection using the anelastic approximation are presented. These calculations span Rayleigh numbers from 10(8)-10(12) for Prandtl number equal to unity, with the fluid density decreasing by a factor of 12 from the bottom to the top of the convection region. This range covers several decades in the "hard" turbulent regime. While many studies of this sort have been conducted for the Boussinesq approximation (i.e., no density stratification), we use the anelastic approximation with a significant density stratification in this turbulent regime. The convection is dominated by a large-scale coherent flow composed of ascending and descending superplumes. We find a power law exponent of 0.28 for the Nusselt-Rayleigh number scaling and a power law with exponent of 0.50 for the Reynolds-Rayleigh number scaling for the entire parameter space studied. These values are very similar to those determined experimentally and analytically for convection with no density stratification.