INSTANTONS AND INTERMITTENCY

We describe the method for finding the non-Gaussian tails of the proba bility distribution function (PDF) for solutions of a stochastic diffe rential equation, such as the convection equation for a passive scalar , the random driven Navier-Stokes equation, etc. The existence of such ails is generally regarded as a manifestation of the intermittency ph enomenon. Our formalism is based on the WKB approximation in the funct ional integral for the conditional probability of large fluctuation. W e argue that the main contribution to the functional integral is given by a coupled field-force configuration-the instanton. As an example, we examine the correlation functions of the passive scalar u advected by a large-scale velocity field delta 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 probabili ty distribution function of high powers of u. We discuss the simplest instantons for the Navier-Stokes equation.