On the internal dynamics of turbulent plumes in the context of stellar convection

We investigate in some details the modeling of turbulent plumes which have been proposed by Rieutord and Zahn to represent the downflows in a stellar convective zone. We show in particular the limits of Taylor's hypothesis about turbulent entrainment and emphasize its connection with the flow's selfsimilarity. The role of the dissipation is shown to be important in the choice of the final asymptotic regime. This is illustrated by a paradox which is solved when dissipation is correctly taken into account. It is concluded that in stellar conditions, the lack of self-similarity implies the replacement of Taylor's hypothesis by a proper closure of the mean-field equations in order to obtain a reliable prediction on the large-scale dynamics.