LAGRANGIAN INSTANTON FOR THE KRAICHNAN MODEL

We consider high-order correlation functions of the passive scalar in the Kraichnan model. Using the instanton formalism, we find the scalin g exponents zn 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 zeta(2) much greater than 1 wher e 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 the n-dependent factors in S-n. (C) 1998 American Institute of Physics. [S0021-3640(98)01319-X].