Equations of energy exchanges in variable density turbulent flows

This paper establishes a new formulation of the energy exchanges between the different parts of total energy. The decomposition uses the Reynolds averaging. This leads to a ternary decomposition of kinetic energy into the turbulence kinetic energy, the mean kinetic energy and the mixed kinetic energy, acting as an exchange term between the mean and turbulent motion. The formulation is then extended to distinguish a mean and fluctuating density part of each part of total energy. The formulation thus includes the mean density turbulence kinetic energy, product of the mean density and the half-trace of the velocity fluctuation correlation tensor. Its evolution equation is given in the spectral domain.