Distribution of stress intensity ratio in canonical turbulent flows and converging-diverging channel

Abstract

The understanding and prediction of wall-bounded turbulence are of great importance for industrial flows. The stress intensity ratio, Rb, is recognized as one key parameter, and its value was known as being around 0.3 in the wake layer of wall-bounded turbulence and the mixing layer. In this work, Rb is studied using Direct Numerical Simulation data extracted from the canonical flows (channel, pipe, flat plate boundary layer at various Reynolds numbers) and converging-diverging channel flow. It is found that in canonical flows and the converging-diverging channel flow, the stress intensity ratio exhibits a certain pattern if the stress intensity ratio varies with the eddy viscosity ratio r or turbulent Reynolds number Rek. Moreover, the r-Rb distribution shows advanced similarity against the Rek-Rb distribution, which is due to that r is consist of transport variables. The similarity is evidenced by the fact that the r-Rb distribution is insensitive to zero pressure gradient, positive pressure gradient, and geometric effects. The r-Rb distribution seems to be mainly sensitive to the friction Reynolds number. This priori study shows that the r-Rb distribution is of universality in flows of different geometric configurations, and it offers information for the construction and improvement of turbulence models.