Self-consistent-field approach to turbulence theory

Abstract

A self-consistent-field type perturbation theory is developed to treat the dynamics of stationary and homogeneous turbulence. The method consists of expanding the full probability distribution function about the product of the exact univariate distributions of all the Fourier modes. The theory is used in second order to find expressions for the turbulent energy spectrum and associated response frequencies. The results for the energy spectrum are identical to a simplified form of the direct-interaction approximation of Kraichnan and closely resemble the results of the generalized random-phase approximation of Edwards. The relation of the present method to both the above approaches is discussed.