A new look at some closure problems of turbulent boundary layers

Abstract

A new look at the closure problem of turbulent boundary layers is made here using recently derived analytical expressions for the shear stress distributions. These expressions are further simplified here and are based on the law of the wall, the law of the wake formulation of Coles (1956) with the mean continuity and the mean momentum differential and integral equations. The concept of equilibrium layers of Clauser (1954, 1956) is extended and using similar ideas as Rotta (1962) for self similarity, a closure scheme is proposed for layers developing in arbitrary adverse pressure gradients for the case where the streamwise derivative of the Coles wake factor is not too large. For a given flow case, this Coles wake condition can be tested with internal consistency checks. The mathematical framework is most suitable for incorporating the attached eddy hypothesis of Townsend (1976) as recently developed by Perry, Li and Marusic (1991) for closure. This gives an opportunity to incorporate coherent structure concepts into closure schemes. Possible ways of handling the difficult case where the streamwise derivative of the Coles wake factor is significant are discussed. Many of the important relations are in analytical form and were derived using Mathematica.

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