Differential diffusion mean scalar gradients

The Reynolds-number dependence of differential-diffusion effects on gap is distinctly different than on pap, and can be best understood by looking at scalars in homogeneous, stationary turbulence with and without uniform mean scalar gradients. 

The case of uniform mean scalar gradients was introduced in Section 3.4, where Gia (see (3.176)) denotes the ith component of the gradient of (< In this section, we will assume that the mean scalar gradients are collinear so that GiaGip = GiaGia = G,pG,p = G2. The scalar covariance production term then reduces to V p = 2rTG2. In the absence of differential diffusion, the two scalars will become perfectly correlated in all wavenumber bands, i.e.,

[Pg.156]

Thus, as noted by Yeung andPope (1993), since the molecular diffusivities do not appear on the right-hand side, molecular differential diffusion affects the coherency only indirectly, i.e., through inter-scale transfer processes which propagate incoherency from small scales to large scales. The choice of the model for the scalar transfer spectra thus completely determines the long-time behavior of pap in the absence of mean scalar gradients. 

Multi-scalar triadic interactions in differential diffusion with and without mean scalar gradients. Journal of Fluid Mechanics 321, 235-278. 

Yeung, P. K. and C. A. Moseley (1995). Effects of mean scalar gradients on differential diffusion in isotropic turbulence. Paper 95-0866, AIAA. 

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