On the evolution of a turbulent boundary layer induced by a three-dimensional roughness element

An experimental investigation is described which has as its objectives the extension of the technical data base pertaining to roughness-induced transition and the advancement of the understanding of the physical processes by which three-dimensional roughness elements induce transition from laminar to turbulent flow in boundary layers. The investigation was carried out primarily with single hemispherical roughness elements surface mounted in a well-characterized zero-pressure-gradient laminar boundary layer on a flat plate. The critical roughness Reynolds number at which turbulence is regarded as originating at the roughness was determined for the roughness elements herein considered and evaluated in the context of data existing in the literature. The effect of a steady and oscillatory free-stream velocity on eddy shedding was also investigated. The Strouhal behaviour of the ‘hairpin’ eddies shed by the roughness and role they play in the evolution of a fully developed turbulent boundary layer, as well as whether their generation is governed by an inflexional instability, are examined. Distributions of mean velocity and intensity of the u -fluctuation demonstrating the evolution toward such distributions for a fully developed turbulent boundary layer were measured on the centreline at Reynolds numbers below and above the critical Reynolds number of transition. A two-region model is postulated for the evolutionary change toward a fully developed turbulent boundary layer: an inner region where the turbulence is generated by the complex interaction of the hairpin eddies with the pre-existing stationary vortices that lie near the surface and are inherent to a flow about a three-dimensional obstacle in a laminar boundary layer; and an outer region where the hairpin eddies deform and generate turbulent vortex rings. The structure of the resulting fully developed turbulent boundary layer is discussed in the light of the proposed model for the evolutionary process.