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Article

Dissipation Statistics of a Passive Scalar in a Multidimensional Smooth Flow

Journal of Statistical Physics. 1999. Vol. 94. No. 5/6. P. 759-777.
Kolokolov I., Gamba A.

We compute analytically the probability distribution function PP(ε) of the dissipation field ε=(∇θ)2 of a passive scalar θ 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→∞, ln PP(ε)∼−(d2ε)1/3.