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

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

2002-05-23

arxiv.org/abs/nlin/0205052v1

Acta Physica Slovaca 52 (2002) 541

Nonlinear Sciences

Chaotic Dynamics

4 pages

Scientific paper

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 $\propto\delta(t-t')/k^{d+\epsilon}$. 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 $\epsilon^3$ of the $\epsilon$ expansion (three-loop approximation).

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