Astronomy and Astrophysics – Astronomy
Scientific paper
Aug 2000
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2000apj...539..469e&link_type=abstract
The Astrophysical Journal, Volume 539, Issue 1, pp. 469-479.
Astronomy and Astrophysics
Astronomy
1
Convection, Methods: Numerical, Sun: Interior, Sun: Rotation
Scientific paper
The dynamics of the convection occurring in the outer 30% by radius of the Sun must determine the transport of energy, angular momentum, and magnetic fields, thereby producing the observed solar differential rotation and playing a strong part in the solar cycle. Attempts to understand the nature of solar convection by analogy with laboratory experiments (e.g., Rayleigh-Bénard convection) are of limited usefulness owing to the large density contrast in the solar convection zone (which cannot be reproduced in the laboratory) and the distributed heating and cooling (produced by the divergence of the radiative flux), which contrasts with the forcing from thermal boundary layers in the laboratory experiments. Given these considerations, numerical simulations appear to provide the best chance of understanding solar convection. Such simulations have typically solved the full Navier-Stokes equation with a greatly enhanced viscosity and the heat transport equation with a constant thermal diffusivity, as well as prescribed temperatures or heat fluxes at the boundaries. Thermal and viscous boundary layers that generate small-scale turbulence tending to fill the computational domain are typically formed. We choose instead to solve the Euler equation and the total energy equation with thermal forcing diagnosed from a standard solar model (but with an extended region of near-surface cooling). We employ the anelastic approximation to filter out sound waves (which play a comparatively small role in convection-zone dynamics owing to the relatively small Mach number) and use a conservative, monotonicity-preserving numerical scheme, which is second-order accurate in smooth regions of the flow and first-order accurate (i.e., dissipative) in rapidly varying regions. We carry out a range of simulations with four different density contrasts up to 30 (which is still modest compared to the value of 107 in the solar convection zone) and at two different numerical resolutions and analyze them paying particular attention to the horizontal scales of the convective structures formed. For the cases with higher density contrasts, we find a small-scale granulation pattern at the surface (whose horizontal scale is proportional to the density scale height) giving way to larger scale plumelike structures in the interior. The horizontal scales of convection are almost insensitive to the numerical resolution, suggesting a good degree of convergence in the results.
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