An alternative formulation of the equations of turbulent motion for a fluid of variable density

The turbulent motion of a fluid of variable density is investigated analytically, regrouping the terms of the standard formulation of the equations of motion into three sets of convective correlations and isolating a flux term which depends on the instantaneous value of the mass density. The mean-value equations for continuity, dynamics, enthalpy, concentration, and kinetic energy are derived; the equations for the principle flows are obtained by analogy to the isovolumetric case; and expressions for kinetic-energy coupling and pressure fluctuations are developed. The secondary terms of the equations and a comparison of terms in the constant-density and variable-density problems are presented in tables.