Theoretical foundations of turbulent flows

Turbulent fluid motions can only be described by constructing more general solutions based on the Liouville equation and it was pointed out that since the Boltzmann equation can be derived from the principles of mechanics and statistics and that this equation can, in principal, describe only laminar motions of fluids. A general approach to obtaining such a solution is outlined based on the concept of groups of particles, some of which can be in an equilibrium state at the same time that others are in a nonequilibrium state. Each group is viewed as a particle-like dynamic entity and a system of coupled collision equations is constructed whose form is similar to the collision equation in the Boltzmann theory but which now describe the kinetics of the system of groups. This system of equations can be reduced to a closed system of equations for describing turbulent motions, in contrast to classical approaches to turbulence which lead to an infinite system which must be truncated.