Abstract
Abstract Systematic methods are developed for deriving closed approximate equations for probability densities of a turbulent velocity field at one and at two points. These methods are based on diagram techniques of non-equilibrium statistical mechanics and quantum field theory. The equations are written down in the weak coupling approximation. Arguments are made that the approximation which is graphically equivalent to the direct-interaction approximation well known in turbulence theory is rather exact when used for deriving closed equations for multipoint distribution functions. Analysis of the equations in the weak coupling approximation in the inertial range shows their compatibility with a local cascade mechanism of energy transfer in wave number space.
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