A turbulent flow over a curved hill Part 1. Growth of an internal boundary layer

Abstract

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.