Diagram equations of the theory of fully developed turbulence

Skeleton diagram equations of turbulence theory – the Dyson equations and the equations for vertices of three types – are obtained nonperturbatively. Their derivation is based on the use of an equation in functional derivatives for the characteristic functional of a hydrodynamic system described by Navier–Stokes equations in the presence of an external random force. The iterative solution of these equations reproduces the perturbation series for second moments that is usually obtained in a more complicated way and also the series for the third moments.