Dissipation statistics of a passive scalar in a multidimensional smooth flow

We compute analytically the probability distribution function ${\cal P}(\epsilon)$ofthedissipationfield$\epsilon =(\nabla \theta)^{2}$ 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 $ϵ\to \mathrm{\infty }$, $\ln {\cal P}(\epsilon)\sim -(d^2\epsilon)^{1/3}$.