2002/05/23 by L. Ts. Adzhemyan, N. V. Antonov, A. N. Vasil'ev
Physics and Astronomy · #nlin.CD
published as Acta Physica Slovaca 52 (2002) 541 · 4 pages
arxiv created 2002/05/23 · arxiv updated 2009/11/30
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 ∝δ(t-t')/kd+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 ε3 of the ε expansion (three-loop approximation).