3-DIMENSIONAL COMPRESSIBLE HYDRODYNAMIC CONVECTION IN THE SUN AND STARS

Using a pseudospectral code, we have obtained numerical solutions of three-dimensional compressible hydrodynamic convection in a stratified medium where the boundaries are open, and where radiative losses are strongest at the top. We do not impose an entrant heat flux from below. Results are presented for a series of three simulations in progressively deeper boxes: the boxes have depths of roughly H(p), 2H(p), and 4H(p) (where H(p) is a pressure scale height). The code does not make the anelastic approximation: rather, it follows sound waves explicitly. The code remains stable for long time intervals: the integration times which have been achieved so far in the three simulations are such that sound waves have time to traverse our grid of order 100 times. By these times, a statistically steady state is well developed in all three cases, with significant upward heat fluxes. The high stability of the code is due in part to the fact that our effective "grid Reynolds' number" is not greatly in excess of unity: as a result, our flows are found to be organized spatially about time-dependent points of convergence and divergence, with convective flows superposed. Moreover, we find spatial organization in the form of vertical "stacking" of smaller structures on top of larger ones, with each structure being roughly H(p) in vertical extent. Compressibility effects are apparent in the density: snapshots indicate that in a horizontal plane, the density at certain points may be of order 10% larger or smaller than elsewhere in that plane. In the context of coronal heating, we are interested in fluxes of kinetic energy, both total fluxes and those in the horizontal direction. Also of interest from the point of view of resonant heating of coronal loops are the spectral distributions of power on a variety of length scales.