A Functional Formulation of the Statistical Theory of Turbulence

Abstract

The Navier–Stokes equation in the presence of external regular and random forces is considered. The statistical solution is described in terms of the characteristic functional obeying the equation in functional derivatives. The representations of corrections to the viscosity and the variance of external random forces due to turbulent mixing have been derived. A relation between the vertices of different types has been found that enables one to take into account the contribution to the physical characteristics of turbulence for vertices of all types.