Conduction in Low Mach Number Flows. I. Linear and Weakly Nonlinear Regimes
Abstract
Thermal conduction is an important energy transfer and damping mechanism in astrophysical flows. Fourier's law, in which the heat flux is proportional to the negative temperature gradient, leading to temperature diffusion, is a wellknown empirical model of thermal conduction. However, entropy diffusion has emerged as an alternative thermal conduction model, despite not ensuring the monotonicity of entropy. This paper investigates the differences between temperature and entropy diffusion for both linear internal gravity waves and weakly nonlinear convection. In addition to simulating the two thermal conduction models with the fully compressible NavierStokes equations, we also study their effects in the reduced "soundproof" anelastic and pseudoincompressible (PI) equations. We find that in the linear and weakly nonlinear regime, temperature and entropy diffusion give quantitatively similar results, although there are some larger errors in the PI equations with temperature diffusion due to inaccuracies in the equation of state. Extrapolating our weakly nonlinear results, we speculate that differences between temperature and entropy diffusion might become more important for strongly turbulent convection.
 Publication:

The Astrophysical Journal
 Pub Date:
 December 2014
 DOI:
 10.1088/0004637X/797/2/94
 arXiv:
 arXiv:1410.5424
 Bibcode:
 2014ApJ...797...94L
 Keywords:

 conduction;
 convection;
 stars: interiors;
 waves;
 Astrophysics  Solar and Stellar Astrophysics;
 Physics  Fluid Dynamics
 EPrint:
 17 pages, accepted to ApJ