Semiconvection: numerical simulations^⋆

¹ Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85748 Garching, Germany
² Faculty of Mathematics, University of Vienna, Nordbergstraße 15, 1090 Vienna, Austria
³ Dept. Aerodynamics and Fluid Mechanics, BTU Cottbus, Siemens-Halske-Ring 14, 03046 Cottbus, Germany
e-mail: florian.zaussinger@tu-cottbus.de

Received: 16 October 2012
Accepted: 18 March 2013

Abstract

A grid of numerical simulations of double-diffusive convection is presented for the astrophysical case where viscosity (Prandtl number Pr) and solute diffusivity (Lewis number Le) are much lower than the thermal diffusivity. As in laboratory and geophysical cases, convection takes place in a layered form. The proper translation of subsonic flows in a stellar interior and an incompressible (Boussinesq) fluid is given, and the validity of the Boussinesq approximation for the semiconvection problem is checked by comparison with fully compressible simulations. The predictions of a simplified theory of mixing in semiconvection given in a companion paper are tested against the numerical results, and used to extrapolate these to astrophysical conditions. The predicted effective He-diffusion coefficient is nearly independent of the double-diffusive layering thickness d. For a fiducial main sequence model (15 M_⊙) the inferred mixing time scale is of the order of 10¹⁰ yr. An estimate for the secular increase in d during the semiconvective phase is given. It can potentially reach a significant fraction of the pressure scale height.