Instanton for the Kraichnan passive scalar problem
Abstract
We consider highorder correlation functions of the passive scalar in the Kraichnan model. Using the instanton formalism we find the scaling exponents ζ_{n} of the structure functions S_{n} for n>>1 under the additional condition dζ_{2}>>1 (where d is the dimensionality of space). At n<n_{c} [where n_{c}=dζ_{2}/2(2ζ_{2})] the exponents are ζ_{n}=(ζ_{2}/4)(2nn^{2}/n_{c}), while at n>n_{c} they are n independent: ζ_{n}=ζ_{2}n_{c}/4. We also estimate ndependent factors in S_{n}, particularly their behavior at n close to n_{c}.
 Publication:

Physical Review E
 Pub Date:
 November 1998
 DOI:
 10.1103/PhysRevE.58.5776
 arXiv:
 arXiv:chaodyn/9803018
 Bibcode:
 1998PhRvE..58.5776B
 Keywords:

 47.27.Ak;
 05.20.y;
 05.40.+j;
 47.10.+g;
 Fundamentals;
 Classical statistical mechanics;
 Nonlinear Sciences  Chaotic Dynamics
 EPrint:
 20 pages, RevTex