Instanton for the Kraichnan passive scalar problem

We consider high-order correlation functions of the passive scalar in the Kraichnan model. Using the instanton formalism we find the scaling exponents zeta(n) of the structure functions S-n for n much greater than 1 under the additional condition d zeta(2) much greater than 1 (where d is the dimensionality of space). At n < n(c) [where n(c) = d zeta(2)/2(2 - zeta(2))] the exponents are zeta(n) = (zeta(2)/4)(2n - n(2)/n(c)), while at n > n(c) they are n independent: zeta(n) = zeta(2)n(c)/4. We also estimate n-dependent factors in S-n, particularly their behavior at n close to n(c). [S1063-651X(98)04011-2].