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Title: CONDUCTION IN LOW MACH NUMBER FLOWS. I. LINEAR AND WEAKLY NONLINEAR REGIMES

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 well-known 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 Navier-Stokes 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.
Authors:
 [1] ; ; ; ;  [2] ;  [3]
  1. Department of Astronomy and Theoretical Astrophysics Center, University of California, Berkeley, CA 94720 (United States)
  2. Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106 (United States)
  3. School of Mathematics and Statistics, University of Sydney, NSW 2006 (Australia)
Publication Date:
OSTI Identifier:
22364855
Resource Type:
Journal Article
Resource Relation:
Journal Name: Astrophysical Journal; Journal Volume: 797; Journal Issue: 2; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ASTROPHYSICS; CONVECTION; DAMPING; DIFFUSION; ENTROPY; EQUATIONS OF STATE; GRAVITY WAVES; HEAT FLUX; MACH NUMBER; NAVIER-STOKES EQUATIONS; NONLINEAR PROBLEMS; STARS; TEMPERATURE GRADIENTS; THERMAL CONDUCTION