Direct interaction approximation for non-Markovianized stochastic models in the turbulence problem

摘要

The purpose of this paper is to explore mathematical aspects associated withthe application of the direct interaction approximation (DIA) (Kraichnan[1],[2]) to the non-Markovianized stochastic models in the turbulence problem.This process is shown to lead to a functional equation, and construction ofsolutions of this equation is addressed within the framework of a continuedfraction representation. The relation of the DIA solution to the perturbativesolution is discussed. The DIA procedure is applied to the problem of wavepropagation in a random medium, which is described by a stochastic differentialequation, with the characteristics of the medium represented by stochasticcoefficients. The results are compared with those given by the perturbativeprocedure.