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A closure scheme is proposed for computing the evolution of turbulent boundary layers developing in arbitrary pressure gradients. Firstly the important parameters pertaining to the flow in the general non-equilibrium case are identified. Then the equations that govern the streamwise evolution of a turbulent boundary layer are formulated in terms of these parameters. This is done by using classical similarity laws such as Prandtl’s law of the wail and Coles’ law of the wake in conjunction with the mean continuity and integral momentum equations. Finally a closure scheme based on empirical data in conjunction with the assumption that the Reynolds shear stress profiles can be described by a two parameter family is used to predieted the evolution for several flow cases and the results compared to experiments.

Streamwise evolution of turbulent boundary layers in arbitrary pressure gradients