Finite-dimensional distribution functions in the statistical theory of turbulence

Closed equations are obtained for the probability densities for the values of the turbulent velocity of an incompressible liquid at one and two points. The methods of nonequilibrium statistical mechanics [1] and quantum field theory [2] are used in the derivation. It is shown that the point of departure in the formalism is an equation of Liouville type with an interaction constant of order unity for all Reynolds numbers. The motives behind the approach to the turbulence problem based on the formalism of finite-dimensional distribution functions are discussed.