The development of turbulent boundary layers with negligible wall stress

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Abstract
In a recent paper, Stratford has described a turbulent boundary layer with continuously zero wall stress and has developed a theory to describe the flow based on two assumptions. The first is that the flow in the outer part of the layer is affected only by the original Reynolds stresses during the initial development, and the second is that flow in the equilibrium layer close to the wall is determined by the pressure gradient and is independent of upstream conditions. In this paper the same assumptions are used, but more careful consideration of their limitations has led to the elimination of some inconsistencies in the original work and to a theory that gives a better description of some of the experimental results. The principal results are: (i) a criterion for zero wall stress in an adverse pressure gradient of sufficient strength, (ii) the form of the pressure distribution for a self-preserving flow with zero stress, (iii) the mean velocity distribution in this flow, (iv) an estimate of the constant in the 'square-root’ velocity distribution for flow near a wall with zero stress.

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