Analytical expressions are obtained for the conditional expected dissipation and the conditional expected diffusion of a passive scalar contaminant in homogeneous turbulent flows by means of several turbulence closures. It is shown that if the single-point probability density function (PDF) of the scalar is represented by the family of exponential distributions, the conditional expected dissipation varies significantly depending on the exponent of the PDF. However, the conditional expected diffusion remains identical. For those members with tails broader than gaussian, the conditional expected dissipation is concave up and for tails narrower than gaussian it is concave down. This is proved mathematically without resorting to asymptotic analysis (of the final stages of mixing) as conducted previously. For all cases, the conditional expected diffusion adopts a linear profile consistent with the linear mean square estimation (LMSE) theory. The similarity of the conditional diffusion field is explained in the context of the "lamellar" theory of turbulent mixing. The mathematical results are in accord with previous results generated by Direct Numerical Simulation (DNS), and are further validated here by comparison with data obtained via the Linear Eddy Model (LEM) of mixing. It is suggested that the behavior of the conditional expected diffusion at the scalar bounds has a significant influence on the evolution of the PDF.
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