Mean-field closure parameters for passive scalar turbulence

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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 tauᵢ from direct numerical simulations. Firstly, we insert the closure ansatz into our equations, assume stationarity, and solve for tauᵢ. Secondly, we use only the closure ansatz itself and obtain tauᵢ 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 Péclet (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.