Penetrative Convection

This movie shows one of our local area convection simulations. The simulation was done at the Pittsburgh Supercomputing Center, on their 512-node Cray T3D. It took over a year to complete this calculation, consuming 285,000 processor-hours in increments of various sizes. About 400 compressed data dumps, of 1.2 GB each, were created. We used a uniform grid of 512**3 cells with periodic boundary conditions in the horizontal directions and with flat, friction free walls at top and bottom. The top wall was held at a constant temperature, and a constant heat flux was introduced through the bottom. Only the top half of this volume was convectively unstable; the bottom half was stable, with the thermal diffusivity smothly varying, as in a real star, to create this transition. The movie shows temperature variations relative the the time averages of temperature for this run at each depth. From hot to cold, the colors run from yellow to red to transparent (neutral temperature) to blue to aqua. Near the bottom of the convection zone, large cold fluctuations are rare, so that this region is largely transparent. This allows one to look into the turbulent convection flow (which we find, by the way, to have a nice Kolmogorov spectrum in the appropriate range of length scales). In the lower half of the volume, this volume rendering shows temperature fluctuations caused by gravity waves driven by the pummeling of the cool, descending plumes (which actually become relatively hot for their depth as they decelerate in the stable region). This movie takes you on a tour, showing the time evolution of the relative temperature over and over (the transitions are noticeable once you understand that this is what is happening. The view from the top shows the many small convection cells there very nicely. Just as mixing length theory would imply, characteristic sizes of convection cells grow larger with depth, so by the time we go half-way down to the bottom of the convection zone, the periodic box is already rather limiting. Other studies show that the typical convection cell near the bottom of the convection zone would like to have at least twice the horizontal extent allowed in this simulation. We knew this, but insisted upon resolving the first several turbulent scales and thus could not afford the billion-cell grid that would have been necessary to give this flow enogh room at all depths to do just what it liked. Rather than do a bigger run of this type we switched to encompassing the entire stellar model with our grid.