M. B. Jones

On the asymptotic similarity of the zero-pressure-gradient turbulent boundary layer

We investigate similarity solutions for the outer part of a zero-pressure-gradient turbulent boundary layer in the limit of infinite Reynolds number. Previous work by George ( Phil. Trans. R. Soc . vol. 365, 2007 p. 789) has suggested that the only appropriate velocity scale for the outer region is U 1 , the free-stream velocity. This is based on the fact that scaling with U 1 leads to a mathematically valid similarity solution of the momentum equation for the outer region in the asymptotic limit of infinite Reynolds number. Here we show that the classical scaling using the friction velocity also leads to a valid similarity solution for the outer flow in this limit. Therefore on this basis it is not possible to dismiss the friction velocity as a possible scaling as has been suggested by George (2007) and others. We show that both the free-stream velocity and the friction velocity are potentially valid scalings according to this theoretical criterion.

Streamwise evolution of turbulent boundary layers in arbitrary pressure gradients

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.