Theoretical principles of turbulent flows

The main hypotheses used in empirical studies of turbulent flows are briefly reviewed, with particular attention given to Navier-Stokes equations, the Reynolds hypothesis, and the kinetic theory of gases based on the Boltzmann equation. Theoretical principles of turbulence are then developed by generalizing the kinetic theory of gases and taking into account recent developments in mechanics and physics. A system of kinetic equations is obtained with allowance for flow inhomogeneities. It is shown that the classical Chapman-Enskog method does not make it possible to obtain closed solutions to the system of equations for mean flow parameters, and the need for using a new method is demonstrated.