We consider high-order correlation functions of the passive scalar in the Kraichnan model. Using the instanton formalism we find the scaling exponents ζn of the structure functions Sn for n>>1 under the additional condition dζ2>>1 (where d is the dimensionality of space). At n<nc [where nc=dζ2/2(2-ζ2)] the exponents are ζn=(ζ2/4)(2n-n2/nc), while at n>nc they are n independent: ζn=ζ2nc/4. We also estimate n-dependent factors in Sn, particularly their behavior at n close to nc.
Physical Review E
- Pub Date:
- November 1998
- Classical statistical mechanics;
- Nonlinear Sciences - Chaotic Dynamics
- 20 pages, RevTex