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Dissipation Statistics of a Passive Scalar in a Multidimensional Smooth Flow

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Abstract

We compute analytically the probability distribution function \(P\)(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 \(P\)(ε)∼−(d 2 ε)1/3.

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Authors and Affiliations

  1. Dipartimento di Matematica, Politecnico di Torino, 10129, Torino, Italy

    Andrea Gamba

  2. Budker Institute, Novosibirsk, 630090, Russia

    Igor V. Kolokolov

Authors
  1. Andrea Gamba
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  2. Igor V. Kolokolov
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Gamba, A., Kolokolov, I.V. Dissipation Statistics of a Passive Scalar in a Multidimensional Smooth Flow. Journal of Statistical Physics 94, 759–777 (1999). https://doi.org/10.1023/A:1004522830805

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  • DOI: https://doi.org/10.1023/A:1004522830805

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