The linear eddy mixing model is used to study effects of the turbulence length‐scale distribution on the transient evolution of a passive scalar in a statistically steady homogeneous turbulent flow. Model simulations are carried out using both wide‐band length‐scale distributions reflecting high‐Reynolds‐number scaling, and narrow‐band (in effect, low‐Reynolds‐number) distributions. The two cases are found to exhibit qualitative differences in mixing behavior. These differences are interpreted mechanistically. The narrow‐band case yields the best agreement with published direct numerical simulation results, suggesting that those results are, in effect, low‐Reynolds‐number results not readily extrapolated to high‐Reynolds‐number mixing.
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Omitted from this discussion is the fact that the random rearrangement process, acting on a scalar field that is initially periodic with period introduces aperiodicity that ultimately results in the development of longer-wavelength components, whose lowest harmonic has period B. Thus, although the final asymptote is as stated in the text, there is an intermediate regime with different behavior. Details will be presented in a future publication.
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A Gaussian PDF corresponds to a uniform distribution of the conditional dissipation over the range of the scalar.12
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