THERMODYNAMICS OF TURBULENCE

The conservation laws and entropy inequality are averaged and corresponding balance laws for the mean turbulent motion are established. The mean flow field is treated as the motion of a two-temperature fluid. The free energy function and coldness of turbulence are introduced and thermodynamics of the mean motion is studied. The averaged Qausius-Duhem inequality is used and constitutive equations for turbulent stress tensor, heat flux and energy flux vectors are formulated. A thermodynamically consistent transport equation for the dissipation rate is also developed. It is shown that the formulation in its simplest form reduces to the common one-and two-equation models of turbulence. An approach for extending the model to include aaisotropy and nonlinear effects is also outlined.