The onset of instability in unsteady boundary-layer separation

The process of unsteady two-dimensional boundary-layer separation at high Reynolds number is considered. Solutions of the unsteady non-interactive boundary-layer equations are known to develop a generic separation singularity in regions where the pressure gradient is prescribed and adverse. As the boundary layer starts to separate from the surface, however, the external pressure distribution is altered through viscous-inviscid interaction just prior to the formation of the separation singularity; hitherto this has been referred to as the first interactive stage. A numerical solution of this stage is obtained here in Lagrangian coordinates. The solution is shown to exhibit a high-frequency inviscid instability resulting in an immediate finite-time breakdown of this stage. The presence of the instability is confirmed through a linear stability analysis. The implications for the theoretical description of unsteady boundary-layer separation are discussed, and it is suggested that the onset of interaction may occur much sooner than previously thought

Unsteady separation past moving surfaces

Unsteady boundary-layer development over moving walls in the limit of infinite Reynolds number is investigated using both the Eulerian and Lagrangian formulations. To illustrate general trends, two model problems are considered, namely the translating and rotating circular cylinder and a vortex convected in a uniform flow above an infinite flat plate. To enhance computational speed and accuracy for the Lagrangian formulation, a remeshing algorithm is developed. The calculated results show that unsteady separation is delayed with increasing wall speed and is eventually suppressed when the speed of the separation singularity approaches that of the local mainstream velocity. This suppression is also described analytically. Only 'upstream-slipping' separation is found to occur in the model problems. The changes in the topological features of the flow just prior to the separation that occur with increasing wall speed are discussed

The structure of a three-dimensional turbulent boundary layer

The three-dimensional turbulent boundary layer is shown to have a self-consistent two-layer asymptotic structure in the limit of large Reynolds number. In a streamline coordinate system, the streamwise velocity distribution is similar to that in two-dimensional flows, having a defect-function form in the outer layer which is adjusted to zero at the wall through an inner wall layer. An asymptotic expansion accurate to two orders is required for the cross-stream velocity which is shown to exhibit a logarithmic form in the overlap region. The inner wall-layer flow is collateral to leading order but the influence of the pressure gradient, at large but finite Reynolds numbers, is not negligible and can cause substantial skewing of the velocity profile near the wall. Conditions under which the boundary layer achieves self-similarity and the governing set of ordinary differential equations for the outer layer are derived. The calculated solution of these equations is matched asymptotically to an inner wall-layer solution and the composite profiles so formed describe the flow throughout the entire boundary layer. The effects of Reynolds number and cross-stream pressure gradient on the cross-stream velocity profile are discussed and it is shown that the location of the maximum cross-stream velocity is within the overlap region

Short-scale break-up in unsteady interactive layers: Local development of normal pressure gradients and vortex wind-up

Following the finite-time collapse of an unsteady interacting boundary layer (step 1), shortened length and time scales are examined here in the near-wall dynamics of transitional-turbulent boundary layers or during dynamic stall. The next two steps are described, in which (step 2) normal pressure gradients come into operation along with a continuing nonlinear critical-layer jump and then (step 3) vortex formation is induced typically. Normal pressure gradients enter in at least two ways, depending on the internal or external flow configuration. This yields for certain internal flows an extended KdV equation with an extra nonlinear integral contribution multiplied by a coefficient which is proportional to the normal rate of change of curvature of the velocity profile locally and whose sign turns out to be crucial. Positive values of the coefficient lead to a further finite-time singularity, while negative values produce a rapid secondary instability phenomenon. Zero values in contrast allow an interplay between solitary waves and wave packets to emerge at large scaled times, this interplay eventually returning the flow to its original, longer, interactive, boundary-layer scales but now coupled with multiple shorter-scale Euler regions. In external or quasi-external flows more generally an extended Benjamin–Ono equation holds instead, leading to a reversal in the roles of positive and negative values of the coefficient. The next step, 3, typically involves the strong wind-up of a local vortex, leading on to explosion or implosion of the vortex. Further discussion is also presented, including the three-dimensional setting, the computational implications, and experimental links

Attenuation technique for measuring sediment displacement levels

A technique for obtaining accurate, high (spatial) resolution measurements of sediment redeposition levels is described. In certain regimes, the method may also be employed to provide measurements of sediment layer thickness as a function of time. The method uses a uniform light source placed beneath the layer, consisting of transparent particles, so that the intensity of light at a point on the surface of the layer can be related to the depth of particles at that point. A set of experiments, using the impact of a vortex ring with a glass ballotini particle layer as the resuspension mechanism, are described to test and illustrate the technique