Intermittent dissipation of a passive scalar in turbulence

Abstract

Probability density function (PDF) of passive scalar dissipation ${\cal P} (ε)$ is found analytically in the limit of large Peclet and Prandtl numbers (Batchelor-Kraichnan regime) in two dimensions. The tail of PDF at $ε\gg<ε>$ is shown to be stretched exponent $\ln{\cal P}(ε)\proptoε^{1/3}$. At $ε\ll<ε>$, ${\cal P}\propto 1/\sqrtε$.