Convection in Slab and Spheroidal Geometries

Three-dimensional numerical simulations of compressible turbulent thermally driven convection, in both slab and spheroidal geometries, are reviewed and analyzed in terms of velocity spectra and mixing length theory. The same ideal gas model is used in both geometries, and resulting ows are compared. The Piecewise-Parabolic Method (PPM), with either thermal conductivity or photospheric boundary conditions, is used to solve the uid equations of motion. Fluid motions in both geometries exhibit a Kolmogorov-like k 5=3 range in their velocity spectra. The longest wavelength modes are energetically dominant in both geometries, typically leading to one convection cell dominating the ow. In spheroidal geometry, a dipolar ow dominates the largest scale convective motions. Down ows are intensely turbulent and updrafts are relatively laminar in both geometries. In slab geometry, correlations between temperature and velocity uctuations, which lead to the enthalpy ux, are fairly independent of depth. In spheroidal geometry this same correlation increases linearly with radius over the inner 70 percent by radius, in which the local pressure scale heights are a sizable fraction of the radius. The e ects from the impenetrable boundary conditions in the slab geometry models are confused with the e ects from non-local convection. In spheroidal geometry non-local e ects, due to coherent plumes, are seen as far as several pressure scale heights from the lower boundary and are clearly distinguishable from boundary e ects. Proceedings of the Fourteenth International Annual Florida Workshop in Nonlinear Astronomy and Physics, \Astrophysical Turbulence and Convection," University of Florida, Feb. 1999 (to appear in the Annals of the New York Academy of Sciences)