The results are presented of a series of computational experiments aimed at studying the characteristics of time-dependent turbulent boundary layers with embedded reversed-flow regions. A calculation method developed earlier was extended to boundary layers with reversed flows for this purpose. The calculations were performed for an idealized family of external velocity distributions, and covered a range of degrees of unsteadiness. The results confirmed those of previous studies in demonstrating that the point of flow reversal is nonsingular in a time-dependent boundary layer. A singularity was observed to develop downstream of reversal, under certain conditions, accompanied by the breakdown of the boundary-layer approximations. A tentative hypothesis was advanced in an attempt to predict the appearance of the singularity, and is shown to be consistent with the calculated results.

Periodic turbulent boundary layers in zero and adverse time-mean pressure gradient have been studied. The study includes experimental, analytical and numerical investigations. The experiments were conducted in an unsteady-flow water tunnel, in which the freestream velocity varies sinusoidally with time around a mean value. Reduced frequencies up to about 25 and a relative oscillation amplitude of 40 per cent of the mean velocity were studied. Flow reversal occurred over a significant part of the oscillation cycle in the adverse pressure gradient experiments, though no mean-flow separation was observed. Data on turbulent stresses and wall shear stress were obtained using a two-component laser Doppler anemometry and a surface-mounted heat flux gage. A theory and calibration procedure were developed for the use of the latter in unsteady flow. All the experimental data were recorded on magnetic tape. A general asymptotic theory has been developed for unsteady turbulent boundary layers. This theory leads to the development of wall functions for these flows. Such wall functions have been developed and used in a calculation procedure based on the k-epsilon model of turbulence.

Recently a new procedure, which solves the governing boundary-layer equations with Keller's box method, has been developed for calculating unsteady laminar flows with flow reversal. In this report, we extend this method to turbulent boundary layers with flow reversal. Using the algebraic eddy viscosity formulation of Cebeci and Smith, we consider several test cases to investigate the proposition that unsteady turbulent boundary layers also remain free of singularities. We also perform turbulent flow calculations by using the turbulence model of Bradshaw, Ferriss, and Atwell; we solve the governing equations for both models by using the same numerical scheme and compare the predictions with each other. The study reveals that, as in laminar flows, the unsteady turbulent boundary layers are free from singularities, but there is a clear indication of rapid thickening of the boundary layer with increasing flow reversal. The study also reveals that the predictions of both turbulence models are the same for all practical purposes. (Author).