Wall turbulence closure based on classical similarity laws and the attached eddy hypothesis

Abstract

A new look at the closure problem of turbulent boundary layers is taken here using recently derived analytical expressions for the shear stress distributions. These expressions are based on the logarithmic law of the wall and law of the wake formulation of Coles [J. Fluid Mech. 1, 191 (1956)] with the mean continuity and the mean momentum differential and integral equations. The concept of equilibrium layers of Clauser [Adv. Mech. 4, 1 (1956)] is extended and using similar ideas as Rotta [Prog. Aeronaut. Sci. 2, 1 (1962)] for self-similarity, a closure scheme is proposed for layers developing in arbitrary pressure gradients for the case where the streamwise derivative of the Coles wake facto..