Mellor, G. L., and D. M. Gibson, 1966: Equilibrium turbulent boundary layers. Journal of Fluid Mechanics, 24 (2), 225-253.

Abstract: Empirical information is extracted from constant-pressure flows and, on this basis alone, the equations of motion are solved for flows where the pressure gradient parameter is held constant. The experimental defect profiles of Clauser and the near-separating profile of Stratford are predicted quite well.
The present work is an extension of the work of Clauser and Townsend in that a particular form for an effective or eddy viscosity is hypothesized. Here, however, a continuous and analytically precise family of defect profiles are calculated for the entire range. The solutions span the whole profile with the exception of the viscous sublayer.
A detailed consideration of the viscous sublayer and a comparative examination of various eddy viscosity hypotheses are included in a companion paper.