Dissipation statistics of a passive scalar in a multidimensional smooth flow

Details Dissipation statistics of a passive scalar in a multidimensional smooth flow Dissipation statistics of a passive scalar in a multidimensional smooth flow

1998-07-31

arxiv.org/abs/chao-dyn/9808001v1

J. Stat. Phys. 94 (1999) 759-777

Physics

Condensed Matter

Statistical Mechanics

Latex, 20 pages, submitted to J. Stat. Phys

Scientific paper

We compute analytically the probability distribution function ${\cal P}(\epsilon)$ of the dissipation field $\epsilon =(\nabla \theta)^{2}$ of a passive scalar $\theta$ advected by a $d$-dimensional random flow, in the limit of large Peclet and Prandtl numbers (Batchelor-Kraichnan regime). The tail of the distribution is a stretched exponential: for $\epsilon \to \infty$, $\ln {\cal P}(\epsilon)\sim -(d^2\epsilon)^{1/3}$.

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