This paper describes a detailed experimental study of turbulent boundary-layer development over rough walls in both zero and adverse pressure gradients. In contrast to previous work on this problem the skin friction was determined by pressure tapping the roughness elements and measuring their form drag.Two wall roughness geometries were chosen each giving a different law of behaviour; they were selected on the basis of their reported behaviour in pipe flow experiments. One type gives a Clauser type roughness function which depends on a Reynolds number based on the shear velocity and on a length associated with the size of the roughness. The other type of roughness (typified by a smooth wall containing a pattern of narrow cavities) has been tested in pipes and it is shown here that these pipe results indicate that the corresponding roughness function does not depend on roughness scale but depends instead on the pipe diameter. In boundary-layer flow the first type of roughness gives a roughness function identical to pipe flow as given by Clauser and verified by Hama and Perry & Joubert. The emphasis of this work is on the second type of roughness in boundary-layer flow. No external length scale associated with the boundary layer that is analogous to pipe diameter has been found, except perhaps for the zero pressure gradient case. However, it has been found that results for both types of roughness correlate with a Reynolds number based on the wall shear velocity and on the distance below the crests of the elements from where the logarithmic distribution of velocity is measured. One important implication of this is that a zero pressure gradient boundary layer with a cavity type rough wall conforms to Rotta's condition of precise self preserving flow. Some other implications of this are also discussed.

An investigation was undertaken to improve our understanding of low-Reynolds-number turbulent boundary layers flowing over a smooth flat surface in nominally zero pressure gradients. In practice, such flows generally occur in close proximity to a tripping device and, though it was known that the flows are affected by the actual low value of the Reynolds number, it was realized that they may also be affected by the type of tripping device used and variations in free-stream velocity for a given device. Consequently, the experimental programme was devised to investigate systematically the effects of each of these three factors independently. Three different types of device were chosen: a wire, distributed grit and cylindrical pins. Mean-flow, broadband-turbulence and spectral measurements were taken, mostly for values of Rθ varying between about 715 and about 2810. It was found that the mean-flow and broadband-turbulence data showed variations with Rθ, as expected. Spectra were plotted using scaling given by Perry, Henbest & Chong (1986) and were compared with their models which were developed for high-Reynolds-number flows. For the turbulent wall region, spectra showed reasonably good agreement with their model. For the fully turbulent region, spectra did show some appreciable deviations from their model, owing to low-Reynolds-number effects. Mean-flow profiles, broadband-turbulence profiles and spectra were found to be affected very little by the type of device used for Rθ ≈ 1020 and above, indicating an absence of dependence on flow history for this Rθ range. These types of measurements were also compared at both Rθ ≈ 1020 and Rθ ≈ 2175 to see if they were dependent on how Rθ was formed (i.e. the combination of velocity and momentum thickness used to determine Rθ). There were noticeable differences for Rθ ≈ 1020, but these differences were only convincing for the pins, and there was a general overall improvement in agreement for Rθ ≈ 2175.

Two experiments were performed to study the response of turbulent boundary layers to sudden changes in surface curvature and pressure gradient. In the first experiment, the behaviour of a boundary layer negotiating a two-dimensional curved hill was examined. Prior to separating on the leeward side of the hill, the layer experienced a short region of concave surface curvature, followed by a prolonged region of convex surface curvature. The corresponding pressure gradient changed from adverse to favourable, and back to adverse. In the second experiment, the flow over a symmetrical wing was studied. This wing had the same profile as the hill with a very similar pressure distribution. The obvious difference between the two experiments was the use of leading and trailing edge plates in the hill flow. The results show that an internal layer forms in the flow over the curved hill, and that this internal layer displays many similarities to the boundary layer observed on the free wing. The internal layer grows as an independent boundary layer beneath a turbulent free-shear layer, and as it develops it establishes its own wall (inner) and wake (outer) regions. The perturbation responsible for initiating the growth of the internal boundary layer seems to be an abrupt change in surface curvature. Once formed, the internal boundary layer dictates the skin-friction distribution and the process of separation over the hill. The effect of the perturbation in wall curvature appears to be different from that due to prolonged convex curvature in that the former affects the flow in the vicinity of the wall instantly, while the latter affects the flow far away from the wall only after the flow turns through some angle. Physical explanations are offered for the qualitative difference between the effects of mild and strong convex curvature, and for the saturated behaviour observed in strongly curved flows. Finally, the results are compared with the behaviour of wind flow over terrestrial hills. In both cases, the internal layer dominates the flow behaviour, even though the scaling laws for the flows over actual hills are not obeyed in the present case. A qualitative comparison reveals that the present internal layer is thicker than that reported in meteorological flows. This appears to be due to the effect of curvature, which perturbs the wake region of the internal layer in the present hill flow, while in meteorological studies the effect of curvature is generally small enough to be neglected.

Smooth- and rough-wall boundary layers and fully developed pipe and duct flow investigations are reviewed. It is shown that the effect of roughness on the flow away from the wall can be accounted for by using an equivalent viscosity νe. This viscosity is thought to depend only on the variables at the wall, such as shear stress τ0, fluid density ρ, viscosity μ and the roughness size and geometry and that the relationship between these variables is the same for both boundary layers and duct flow. However, experiments to date have been confined to the ‘rough régime’ and to boundary layers with a zero pressure gradient.Experiments were performed and the results show that the above finding can be extended to boundary layers with adverse pressure gradients in the rough régime.A general method for measuring the local boundary-layer characteristics, with roughness and pressure gradients present, is developed.

An attempt has been made to establish the laws governing the flow in a turbulent line vortex. Up to the present time theoretical solutions for laminar flow have been used for comparison with experimental results for turbulent flow to find an ‘eddy viscosity’ term and its variation with various parameters. An approach is developed along lines similar to the methods used in turbulent boundary-layer theory and is found to be reasonably successful as far as the work has proceeded. It is predicted by theory, and confirmed by experiment, that the circulation in the vortex is proportional to the logarithm of radius under certain conditions. For the present experimental conditions, the vortices are found to be completely independent of viscosity effects when the parameter WZ/K0 exceeds 150, and above this value the experimental results may be correlated to give a universal distribution of circulation in the inner region of the vortex. Further experiments are necessary to verify and extend the results of these tests before any definite conclusions may be made regarding the circulation distribution in the outer core region of the vortex and the growth and development of the vortex.