Statistical equations for turbulent compressible fluids

The statistical equations of fluids with variable densities in turbulent flows are written first in general form (Favre, 1969, 1971, 1972), and then by choosing from these forms complementary definitions for decomposition of aleatory quantities into macroscopic parts and for fluctuations which lead to the most suitable expressions. These equations express the balance of mass, the balance of quantity of motion, the balance of energy, and the balance of entropy of the fluid. The present work also employs equations of state, as well as relations concerning the physical properties of the fluid (such as viscosity, thermal conductivity, molecular diffusivity, and specific heat). Generalities on the theory behind these equations and on the statistical balance of transportable quantities precede the analysis.