Higher corrections to the direct interaction approximation in turbulence theory

The next higher approximation to the direct interaction approximation is calculated making use of an approach to the turbulent equations which has been reported earlier. The equations of turbulence are interpreted as stochastic equations and an ordering scheme is set up which depends on increasingly indirect feedback of a mode on itself. In the lowest approximation, the direct interaction approximation is recovered. A calculation of the next higher approximation beyond the direct interaction approximation is presented. The higher approximations are of increasing order and are a formal expansion in "powers" of Green's functions which appear in convolution integrals.