Dynamics and scaling of Reynolds shear stress in adverse pressure-gradient flows

Abstract

Using a dynamical transport analysis for the turbulence momentum, the Reynolds stress gradient can be expressed as a function of the local momentum flux and force terms for adverse pressure-gradient flows. From the perspective of an observer moving at the local mean velocity, Reynolds stress gradient is seen to represent the lateral transport of streamwise momentum, balanced by the u’² transport, pressure and viscous force terms. Data sets (Soria et al., 2020; Gungor et al. [6]; Rkein and Laval [22]) from direct numerical simulations (DNS) are used to validate this method for adverse pressure-gradient boundary layer flows, with a good degree of consistency and agreements. Reynolds shear stress profile, in its full attributes and minor fluctuations, are replicated through the Lagrangian momentum equation. Gradient analysis also leads to scaling at the first- and second-derivative levels, for u’², v’² and u’v’. These findings lead to both quantitative prescription and insights on the origin of the Reynolds shear stress structure in adverse pressure-gradient flows.