Unsteady turbulent boundary layers with flow reversal
A theoretical study is carried out to search for the appearance of a singularity in a family of time-dependent turbulent boundary layers with embedded reverse-flow regions and determine the conditions necessary for its appearance. Further insight is gained into the development of unsteady turbulent boundary layers. The calculations performed for a family of prescribed external velocity distributions in which the relative importance of the effects of time-dependence, compared to those of spatial diffusion, are controlled by a given parameter. The conditions necessary for the appearance of a singularity appears to involve the existence of an appropriate relationship between the dominant velocities in the reversed-flow region and the rate of forward movement of the flow reversal point. The results support the hypothesis that a singularity will exist in the flow if and only if the typical reversed-flow velocities exceed the rate of penetration of the reversed flow into the oncoming boundary layer.