1996/09/27 by Alain Pumir, Pumir, Alain, Boris I. Shraiman +3
Physics and Astronomy · #Condensed Matter (cond-mat) #FOS: Physical sciences #cond-mat
paper · pdf · doi:10.48550/arxiv.cond-mat/9609272
arxiv created 1996/09/27 · arxiv updated 2009/11/30
The third order correlation function of the scalar field advected by a Gaussian random velocity, with a spatial scaling exponent 2 - ε, and in the presence of a mean gradient, is calculated perturbatively in ε<< 1. This expansion corresponds to the regime close to Batchelor's advection by linear diffeomorphisms. The scaling exponent is found to be equal to 1 in dimensions 2 and 3, up to corrections smaller than \cal O ( ε) , implying an anomalous scaling of the third order correlation function and the persistence of small scale anisotropy.