Dissipation statistics of a passive scalar in a multidimensional smooth flow

Abstract

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 $\epsilon \to \infty$, $\ln {\cal P}(\epsilon)\sim -(d^2\epsilon)^{1/3}$.