Instantons and intermittency
Abstract
We describe the method for finding the nonGaussian tails of the probability distribution function (PDF) for solutions of a stochastic differential equation, such as the convection equation for a passive scalar, the random driven NavierStokes equation, etc. The existence of such tails is generally regarded as a manifestation of the intermittency phenomenon. Our formalism is based on the WKB approximation in the functional integral for the conditional probability of large fluctuation. We argue that the main contribution to the functional integral is given by a coupled fieldforce configurationthe instanton. As an example, we examine the correlation functions of the passive scalar u advected by a largescale velocity field δ correlated in time. We find the instanton determining the tails of the generating functional, and show that it is different from the instanton that determines the probability distribution function of high powers of u. We discuss the simplest instantons for the NavierStokes equation.
 Publication:

Physical Review E
 Pub Date:
 November 1996
 DOI:
 10.1103/PhysRevE.54.4896
 arXiv:
 arXiv:chaodyn/9512006
 Bibcode:
 1996PhRvE..54.4896F
 Keywords:

 47.10.+g;
 47.27.i;
 05.40.+j;
 Turbulent flows;
 Nonlinear Sciences  Chaotic Dynamics;
 Condensed Matter;
 High Energy Physics  Theory
 EPrint:
 15 pages, REVTEX 3.0