Lagrangian instanton for the Kraichnan model

Balkovsky E., Lebedev V.

PACS: 05.40.+j, 47.10.+g, 47.27.-i

**We consider high-order correlation functions of the passive scalar in the Kraichnan model. Using the instanton formalism we find the scaling exponents ***ζ*_{η} of the structure functions *S*_{n} for η ^> 1 under the additional condition *άζι *^> 1 (where *d *is the dimensionality of space). At η < n_{c} (where *n*_{c} — ^/[2(2 **— ****£2)]) the exponents are ***ζη ***— ****(C2/4)(2n ****— ***n*^{2}/n_{c})_{y} while at η > *n*_{c} they are η-independent: *ζ*_{η} = óÇ«Å**/4« We also estimate η-dependent factors**