Homogeneous Turbulence Two-Point Closures and Applications to One-Point Closures,

This paper deals with homogeneous, i.e. translation invariant, turbulence. Homogeneous turbulence is an ideal situation in which the mean field is unaffected by the turbulent motion, so that the turbulent motion can be studied solely with a prescribed mean field. Such a flow can nearly be achieved in very simple experimental set-ups. Fourier transforms are convenient to study the turbulent motion. The momentum equation shows that the evolution of the turbulent motion is due, on the one hand, to the action of turbulence upon itself nonlinear effects and, on the other hand, to the action of the mean field upon turbulence linear effects. The linear problem can be solved with the help of a GREEN function. Some important solutions are then studied. The nonlinear problem is open and requires modelling. Various approaches are described, in the simple case of homogeneous isotropic turbulence. The resolution of the transport equation for the REYNOLDS stresses requires the closure of the pressure strain terms and of the dissipation equation. Application of two-point closures to the modelling of these terms is studied in the last part.