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Renormalization group, operator product expansion and anomalous scaling in models of passive turbulent advection

L. Ts. Adzhemyan·N. V. Antonov·A. N. Vasil'ev
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Abstract

The field theoretic renormalization group is applied to Kraichnan's model of a passive scalar quantity advected by the Gaussian velocity field with the pair correlation function $\proptoδ(t-t')/k^{d+ε}$. Inertial-range anomalous scaling for the structure functions and various pair correlators is established as a consequence of the existence in the corresponding operator product expansions of ``dangerous'' composite operators (powers of the local dissipation rate), whose {\it negative} critical dimensions determine anomalous exponents. The latter are calculated to order $ε^3$ of the $ε$ expansion (three-loop approximation).

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L. Ts. Adzhemyan, N. V. Antonov, A. N. Vasil'ev. 2002-05-23. Renormalization group, operator product expansion and anomalous scaling in models of passive turbulent advection. https://arxiv.org/abs/nlin/0205052

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