The Lagrangian spectral relaxation model for differential diffusion in homogeneous turbulence

The Lagrangian spectral relaxation (LSR) model is extended to treat turbule nt mixing of two passive scalars (phi(alpha) and phi(beta)) with different molecular diffusivity coefficients (i.e., differential-diffusion effects). Because of the multiscale description employed in the LSR model, the scale dependence of differential-diffusion effects is described explicitly, inclu ding the generation of scalar decorrelation at small scales and its backsca tter to large scales. The model is validated against DNS data fur different ial diffusion of Gaussian scalars in forced, isotropic turbulence at four v alues of the turbulence Reynolds number (R-lambda = 38, 90, 160, and 230) w ith and without uniform mean scalar gradients. The explicit Reynolds and Sc hmidt number dependencies of the model parameters allows for the determinat ion of the Re (integral-scale Reynolds number) and Sc (Schmidt number) scal ing of the scalar difference z = phi(alpha) - phi(beta). For example, its v ariance is shown to scale like [z(2)] similar to Re-0.3. The rate of backsc atter (beta(D)) from the diffusive scales towards the large scales is found to be the key parameter in the model. In particular, it is shown that beta (D) must be an increasing function of the Schmidt number for Sc less than o r equal to 1 in order to predict the correct scalar-to-mechanical time-scal e ratios, and the correct long-time scalar decorrelation rate in the absenc e of uniform mean scaler gradients. (C) 1999 American Institute of Physics. [S1070-6631(99)01706-7].