Intermittent Dissipation of a Passive Scalar in Turbulence

The probability density function (PDF) of passive scalar dissipation $P\left(\epsilon \right)$ is found analytically in the limit of large Peclet and Prandtl numbers (Batchelor-Kraichnan regime) in two dimensions. The tail of PDF at $\epsilon \gg 〈\epsilon 〉$ is shown to be stretched exponent $\ln P\left(\epsilon \right)\propto {\epsilon }^{1/3}$; at $\epsilon \ll 〈\epsilon 〉$, $P\propto 1/\sqrt{\epsilon }$.