On negative turbulence production phenomena in the shear layer of separating and reattaching flows

Abstract The analysis of Direct Numerical Simulation data of the separating and reattaching flow over a blunt bluff body with sharp edges, reveals the presence of negative turbulence production mechanisms in the leading-edge shear layer. Contrary to what is commonly observed in fully developed turbulent flows, this phenomenon represents flow reversal of energy from the fluctuating field to the mean flow. The detailed study of the data reveals that at the origin of such mechanisms is a statistically positive relation between Reynolds shear stresses and vertical shear. We argue that such a positive relation is a result of large-scale interactions of the fluctuating field with the streamwise inhomogeneity. The analysis of time cospectra confirms this picture by highlighting the presence of a net separation of scales consisting in a range of small scales positively contributing to turbulence production in opposition to a range of large scales giving to a reversal of flow energy from the fluctuating to the mean field. By means of a reduced description of the interactions of the fluctuating field with the mean field given by a generalized mixing length hypothesis, we finally also provide conceptual arguments for the modelling of turbulence production in the transitional shear layer. A model for the mixing length is also proposed which is found to work nicely in shear flows. The simplicity of the formulation supports its use especially in experiments of wall-bounded turbulence.