On the Kraichnan Model of Passive Scalar Advection Near the Batchelor   limit
  The third order correlation function of the scalar field advected by a Gaussian random velocity, with a spatial scaling exponent $2 - \epsilon$, and in the presence of a mean gradient, is calculated perturbatively in $\epsilon << 1$. 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 } ( \epsilon ) $, implying an anomalous scaling of the third order correlation function and the persistence of small scale anisotropy. 
Alain Pumir (Institut Non Lineaire de Nice), Boris I. Shraiman (Bell   Laboratories), Eric D. Siggia (Cornell University)