Description
Plumes are considered to play an important role in the transport in stellar convection. The non-equilibrium effect associated with plumes is linked to the variations of turbulence properties along the plume motions. With the response-function formulation of the renormalised perturbation theory, the non-equilibrium properties of turbulence can be incorporated into the analytical expressions of the turbulent fluxes such as the turbulent mass flux, the Reynolds and turbulent Maxwell stresses, and the turbulent heat/energy flux. A turbulence model with this non-equilibrium effect incorporated is proposed. This non-equilibrium turbulence model is applied to a two convection configurations: the locally or entropy-gradient driven convection and the non-locally or surface-cooling driven convection. The validation of the non-equilibrium turbulence model is sought in these two cases by comparing the results of turbulence model with those of direct numerical simulations (DNSs). The statistical and mean properties of turbulence in the two convection configurations are discussed, including the analysis of the probability distribution function and the turbulent energy flux.
