Abstract
A class of phenomenological Hopf equations describing mixing of a passive scalar by random flow close to the Batchelor limit ~i.e., advection by random strain and vorticity! is analyzed. In the Batchelor limit multipoint correlators of the scalar are constructed explicitly by exploiting the SL ( N,R) symmetry of the Hopf operator. Hopf equations close to this ‘‘integrable’’ limit are solved via singular perturbation theory based on matched asymptotic expansions. The solution for the three-point correlator exhibits anomalous scaling indicating persistence of the small scale anisotropy for the scalar. In addition to the exponent, the full configuration dependence of the correlator is obtained. @S1063-651X~98!08703-0# PACS number~s!: 47.27.2i
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