Anomalous Scaling Exponents of a White-Advected Passive Scalar

1995/09/30 by M. Chertkov, G. Falkovich · 1 citation
Physics and Astronomy · #chao-dyn #cond-mat #hep-th #nlin.CD

paper · pdf · doi:10.1103/physrevlett.76.2706

4 pages, RevTex 3.0, Submitted to Phys. Rev. Lett

arxiv created 1996/01/19 · arxiv updated 2009/11/30

Abstract

For Kraichnan's problem of passive scalar advection by a velocity field delta-correlated in time, the limit of large space dimensionality d≫1 is considered. Scaling exponents of the scalar field are analytically found to be ζ_2n=nζ₂-2(2-ζ₂)n(n-1)/d, while those of the dissipation field are μ_n=-2(2-ζ₂)n(n-1)/d for orders n≪ d. The refined similarity hypothesis ζ_2n=nζ₂+μ_n is thus established by a straightforward calculation for the case considered.

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