Instability in a viscous flow driven by streamwise vortices

Abstract

Unsteady separation processes at large finite, Reynolds number, Re , are considered, as well as the possible relation to existing descriptions of boundary-layer separation in the limit Re → ∞. The model problem is a fundamental vortex-driven three-dimensional flow, believed to be relevant to bursting near the wall in a turbulent boundary layer. Bursting is known to be associated with streamwise vortex motion, but the vortex/wall interactions that drive the near-wall flow toward breakdown have not yet been fully identified. Here, a simulation of symmetric counter-rotating vortices is used to assess the influence of sustained pumping action on the development of a viscous wall layer. The calculated solutions describe a three-dimensional flow at finite Re that is independent of the streamwise coordinate and consists of a crossflow plane motion, with a developing streamwise flow. The unsteady problem is constructed to mimic a typical cycle in turbulent wall layers and numerical solutions are obtained over a range of Re . Recirculating eddies develop rapidly in the near-wall flow, but these eddies are eventually bisected by alleyways which open up from the external flow region to the wall. At sufficiently high Re , an oscillation was found to develop in the streamwise vorticity field near the alleyways with a concurrent evolution of a local spiky behaviour in the wall shear. Above a critical value of Re , the oscillation grows rapidly in amplitude and eventually penetrates the external flow field, suggesting the onset of an unstable wall-layer breakdown. Local zones of severely retarded streamwise velocity are computed which are reminiscent of the low-speed streaks commonly observed in turbulent boundary layers. A number of other features also bear a resemblance to observed coherent structure in the turbulent wall layer.