On the Kraichnan Model of Passive Scalar Advection Near the Batchelor limit

Details On the Kraichnan Model of Passive Scalar Advection Near the Batchelor limit On the Kraichnan Model of Passive Scalar Advection Near the Batchelor limit

1996-09-27

arxiv.org/abs/cond-mat/9609272v1

Physics

Condensed Matter

Scientific paper

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.

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