Non-Fickian diffusion and tau approximation from numerical turbulence

Evidence for non-Fickian diffusion of a passive scalar is presented using direct simulations of homogeneous isotropic turbulence. The results compare favorably with an explicitly time-dependent closure model based on the tau approximation. In the numerical experiments three different cases are considered: (i) zero mean concentration with finite initial concentration flux, (ii) an initial top hat profile for the concentration, and (iii) an imposed background concentration gradient. All cases agree in the resulting relaxation time in the tau approximation relating the triple correlation to the concentration flux. The first order smoothing approximation is shown to be inapplicable.