A Priori Validation of Subgrid-scale Models for Astrophysical Turbulence

Abstract

Abstract We perform a priori validation tests of subgrid-scale (SGS) models for the turbulent transport of momentum, energy, and passive scalars. To this end, we conduct two sets of high-resolution hydrodynamical simulations with a Lagrangian code: an isothermal turbulent box with rms Mach numbers of 0.3, 2, and 8, and the classical wind tunnel where a cold cloud traveling through a hot medium gradually dissolves due to fluid instabilities. Two SGS models are examined: the eddy diffusivity (ED) model widely adopted in astrophysical simulations and the “gradient model” due to Clark et al. We find that both models predict the magnitude of the SGS terms equally well (correlation coefficient >0.8). However, the gradient model provides excellent predictions for the orientation and shape of the SGS terms while the ED model predicts both poorly, indicating that isotropic diffusion is a poor approximation to the instantaneous turbulent transport. The best-fit coefficient of the gradient model is in the range of [0.16, 0.21] for the momentum transport, and the turbulent Schmidt number and Prandtl number are both close to unity, in the range of [0.92, 1.15].