A Reynolds Stress Function for Wall Layers

Abstract

Data for the Reynolds stress near a wall are correlated by employing the theory of perturbation methods to form a composite expansion. This absorbs, to first order, the effects of Reynolds number. Published data from three experimental and three direct numerical simulations of channel flow and one experimental and two direct numerical simulations of pipe flow were examined. A single curve fits the results to within the scatter of the data. If Reynolds number effects exist, they are hidden in the scatter. A closed-form equation, with one arbitrary constant, represents the data and has the proper limiting behavior both very near and very far from the wall.