1995/12/31 by Gregory Falkovich, I. V. Kolokolov, В. В. Лебедев +1 · 2 citations
Engineering · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Fluid Dynamics and Turbulent Flows #Statistical Mechanics and Entropy
paper · doi:10.1103/physreve.54.4896
openalex publication_date 1996/11/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We describe the method for finding the non-Gaussian 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 Navier-Stokes 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 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 \ensuremathδ 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 Navier-Stokes equation. \textcopyright 1996 The American Physical Society.