Direct numerical simulations of isotropically forced homogeneous stationary turbulence with an imposed passive scalar concentration gradient are compared with an analytical closure model which provides evolution equations for the mean passive scalar
flux and variance. Triple correlations of fluctuations appearing in these equations are described in terms of relaxation terms proportional to the quadratic correlations. Three methods are used to extract the relaxation timescales tau_i from direct numerical simulations. Firstly, we insert the closure ansatz into our equations, assume stationarity, and solve for tau_i. Secondly, we use only the closure ansatz itself and obtain tau_i from the ratio of quadratic and triple correlations. Thirdly we remove the imposed passive scalar gradient and fit an exponential decay law to the solution. We vary the Reynolds (Re) and Peclet (Pe) numbers while keeping their ratio at unity and the degree of scale separation and find for large Re fair correspondence between the different methods. The ratio of the turbulent relaxation time of passive scalar flux to the turnover time of turbulent eddies is of the order of three, which is in remarkable agreement with earlier work. Finally we make an effort to extract the relaxation timescales relevant for the viscous and diffusive effects. We find two regimes which are valid for small and large Re, respectively, but the dependence of the parameters on scale separation suggests that they are not universal.
We determine the timescales associated with turbulent diffusion and isotropization in closure models using anisotropically forced and freely decaying turbulence simulations and to study the applicability of these models. We compare the results from a
nisotropically forced three-dimensional numerical simulations with the predictions of the closure models and obtain the turbulent timescales mentioned above as functions of the Reynolds number. In a second set of simulations, turning the forcing off enables us to study the validity of the closures in freely decaying turbulence. Both types of experiments suggest that the timescale of turbulent diffusion converges to a constant value at higher Reynolds numbers. Furthermore, the relative importance of isotropization is found to be about 2.5 times larger at higher Reynolds numbers than in the more viscous regime.
