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 number 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 wildly adopted in astrophysical simulations and the “ gradient model ” due to \citet 1979JFM….91….1C .
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 on the orientation and shape of the SGS terms while the ED model predicts poorly on both , indicating that isotropic diffusion is a poor approximation of 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 ] .