The role of the inhomogeneous pressure-strain in transition and turbulence*

Mixing at the interface between two materials occurs in a variety of important applications such as atmospheric, oceanic and astrophysical. When subjected to a rapid acceleration, an initially laminar interface will transition from laminar to turbulent flow. Although current variable density turbulence models behave well for fully turbulent flows, they often perform inadequately during transition. One key component to capture the transition process is the proper modeling of the velocity pressure-gradient correlation, which is usually split into pressure strain and pressure diffusion terms. Although for fully turbulent flows the inhomogeneous contribution to the pressure-strain term is generally neglected, this cannot be done during transition where the flow can be highly inhomogeneous. Using the Green's function solution to the pressure Poisson equation, we derive semi-analytical expressions for the pressure strain and pressure diffusion models. The pressure strain model is shown to be composed of homogeneous and inhomogeneous components. These are subsequently evaluated numerically using linear stability theory and direct numerical simulation data for the entire mixing process. This approach allows to assess the validity of the new models and to provide new insights on the relative importance of the homogeneous and inhomogeneous components of the pressure strain model during the transitional and fully turbulent regimes.