SEPARATION OF VARIABLES AND FLUID-MOMENT EXPANSION OF A TWO-PARTICLE KINETIC EQUATION

The two-particle BBGKY equation with the assumption of "three-particle" molecular chaos is separated into a one-particle equivalent through the method of variable separation. Fluid moment expansion of the equation yields equations which govern Reynolds stress and turbulent heat transfer. These equations are characterized by having dual time dependence responsible for stochastic and coherent facets of turbulent fluctuations. Their consistency with the phenomenological fluid equations is indicated. The key role of the kinetic theory lies in imposing a constraint in addition to being consistent with the Navier-Stokes regime. The obtained set of equations proves to be the unique one singled out of multiple candidates equally eligible otherwise as governing the Reynolds stress.