On Functional Formulation of the Statistical Theory of Homogeneous Turbulence and the Method of Skeleton Feynman Diagrams

Abstract

The formalism of characteristic functional is applied for statistical description of a random velocity field obeyed the Navier-Stokes equations in the presence of regular and random external forces. The equation in functional derivatives for characteristic functional was obtained with the help a representation of characteristic functional in the form of functional integral over two fields From this equation one can get equations for various characteristics of velocity field such as the variance of velocity pulsations or for a mean response of the velocity field to external forcing (Green’s function). In the analyses of the solution structures it was used the method of skeleton Feynman diagrams followed directly from the functional formulation of the theory without referring to commonly used perturbation theory methods.