Direct Interaction Approximation for Non-Markovianized Stochastic Models in the Turbulence Problem
Abstract
The purpose of this paper is to explore mathematical aspects associated with the 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 of solutions of this equation is addressed within the framework of a continued fraction representation. The relation of the DIA solution to the perturbative solution is discussed. The DIA procedure is applied to the problem of wave propagation in a random medium, which is described by a stochastic differential equation, with the characteristics of the medium represented by stochastic coefficients. The results are compared with those given by the perturbative procedure.
Cite
@article{arxiv.1709.08069,
title = {Direct Interaction Approximation for Non-Markovianized Stochastic Models in the Turbulence Problem},
author = {B. K. Shivamoggi and N. Tuovila},
journal= {arXiv preprint arXiv:1709.08069},
year = {2017}
}