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Normal and anomalous scaling of the fourth-order correlation function of a randomly advected passive scalar

M. Chertkov, G. Falkovich, I. Kolokolov, and V. Lebedev

  • Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel
  • Universite di Milano, Istituto Nacional de Fisica Nucleare, via Celoria 16, Milano 20133, Italy
  • Budker Institute of Nuclear Physics, Novosibirsk 630090, Russia
  • Landau Institute for Theoretical Physics, Moscow, Kosygina 2, 117940, Russia

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Phys. Rev. E 52, 4924 – Published 1 November, 1995

DOI: https://doi.org/10.1103/PhysRevE.52.4924

Abstract

For a δ-function-correlated velocity field, simultaneous correlation functions of a passive scalar satisfy closed equations. We analyze the equation for the four-point function. To describe a solution completely, one has to solve the matching problems at the scale of the source and at the diffusion scale. We solve both the matching problems and thus find the dependence of the four-point correlation function on the diffusion and pumping scale for large space dimensionality d. It is shown that anomalous scaling appears in the first order of 1/d perturbation theory. Anomalous dimensions are found analytically both for the scalar field and for its derivatives, in particular, for the dissipation field.

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Outline

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Phys. Rev. E 52, 4924– Published 1 November, 1995
  • Received 3 August 1995

© 1995 American Physical Society

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