Similarity analysis for turbulent boundary layer with pressure gradient: Outer flow

The equilibrium-type similarity analysis of George and Castillo for the outer part of zero pressure gradient boundary layers (George, W.K., and Castillo, L., Zero Pressure Gradient Turbulent Boundary Layer, Applied Mechanics Reviews, Pt. 1, Vol. 50, No, 11, 1997, pp, 689-729) has been extended to include boundary layers with pressure gradient, The constancy of a single new pressure gradient parameter is all that is necessary to characterize these new equilibrium turbulent boundary layers. Three major results are obtained: First, most pressure gradient boundary experiments appear to be equilibrium flows (by the new definition), and nonequilibrium Rows appear to be the exception. Second, there appear to be only three values of the pressure gradient parameter: one for adverse pressure gradients, one for favorable pressure gradients, and one for zero pressure gradients, Third, correspondingly, there appear to be only three normalized velocity deficit profiles, exactly as suggested by the theory.