Three-dimensional simulations of turbulent compressible convection

Three-dimensional simulations of turbulent and fully compressible thermal c onvection in deep atmospheres are presented and analyzed in terms of veloci ty power spectra, mixing-length theory, and production of vorticity. Densit y contrasts across these convective layers are typically around 11. The flu id model is that of an ideal gas with a constant thermal conductivity. The piecewise parabolic method (PPM), with thermal conductivity added in, is us ed to solve the fluid equations of motion. No explicit viscosity is include d, and the low numerical viscosity of PPM leads to a very low effective Pra ndtl number and very high effective Rayleigh number. Mesh resolutions range as high as 512 x 512 x 256, and the corresponding effective large-scale Ra yleigh numbers range as high as 3.3 x 10(12). Compressional effects lead to intensely turbulent downflow lanes and relatively laminar updrafts, especi ally near the top boundary. The enstrophy contrast between downflows and up flows increases with mesh resolution (and hence with decreasing viscosity) and ranges as high as a factor of 30 in our highest resolution model. Vorti city is everywhere preferentially aligned with the principal direction of s train associated with the large-scale circulation. Near the top boundary, t he strain held associated with the largest scale of convection dominates, w hich leads to a two-dimensional horizontal network of vortex tubes. For the same reason, both the upper portions of the downflow lanes and the lower p ortions of the updrafts contain many strong vertical vortex tubes with heli cities of random sign. The horizontal vortex tubes near the very top of the downflow lanes tend to come in counterrotating pairs, with one on each sid e of the downflow lane. Therefore, as with observations of the Sun, there a re upflows along each side of the prominent downflows in our simulations. M ach numbers in these convective layers are largest in the upper, more diffu se region. There they range as high as 0.8, which significantly modifies th e pressure and gravitational force balance from that which would apply unde r static conditions. This effect is incorporated into our mixing-length ana lysis of the simulation data.