Calculation of the anomalous exponents in the rapid-change model of passive scalar advection to order ε³

2001/06/15 by L. Ts. Adzhemyan, N. V. Antonov, V. A. Barinov +2 · 1 citation
Physics and Astronomy · #nlin.CD

paper · pdf · doi:10.1103/physreve.64.056306

published as Phys. Rev. E64: 056306 (2001) · 34 pages, 5 figures, REVTeX

arxiv created 2001/06/15 · arxiv updated 2009/11/30

Abstract

The field theoretic renormalization group and operator product expansion are applied to the model of a passive scalar advected by the Gaussian velocity field with zero mean and correlation function ∝δ(t-t')/k^d+\eps. Inertial-range anomalous exponents, identified with the critical dimensions of various scalar and tensor composite operators constructed of the scalar gradients, are calculated within the ε expansion to order ε³ (three-loop approximation), including the exponents in anisotropic sectors. The main goal of the paper is to give the complete derivation of this third-order result, and to present and explain in detail the corresponding calculational techniques. The character and convergence properties of the ε expansion are discussed; the improved ``inverse'' ε expansion is proposed and the comparison with the existing nonperturbative results is given.

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