  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 Clark et al. (1979). 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].
