3-D Simulations of Turbulent Compressible Convection

Three{dimensional simulations of turbulent and fully compressible thermal convection in deep atmospheres are presented and analyzed in terms of velocity power spectra, mixing{length theory, and production of vorticity. Density contrasts across these convective layers are typically around 11. The uid model is that of an ideal gas with a constant thermal conductivity. The Piecewise-Parabolic Method (PPM), with thermal conductivity added in, is used to solve the uid equations of motion. No explicit viscosity is included, and the low numerical viscosity of PPM leads to a very low e ective Prandtl number and very high e ective Rayleigh number. Mesh resolutions range as high as 512 512 256, and the corresponding e ective large{scale Rayleigh numbers range as high as 3:3 10. Compressional e ects lead to intensely turbulent down ow lanes and relatively laminar updrafts, especially near the top boundary. The enstrophy contrast between down ows and up ows increases with mesh resolution (and hence with decreasing viscosity), and ranges as high as a factor of 30 in our highest resolution model. Vorticity is everywhere preferentially aligned with the principal direction of strain associated with the large{scale circulation. Near the top boundary, the strain eld associated with the largest scale of convection dominates, which leads to a 2-D horizontal network of vortex tubes. For the same reason, both Laboratory for Computational Science and Engineering, University of Minnesota, Minneapolis, MN 55455