THE BOUNDARY-LAYER FLOW DUE TO A VORTEX APPROACHING A CYLINDER

The three-dimensional unsteady boundary layer induced by a vortex fila ment moving outside a circular cylinder is considered. In the present paper, we focus attention on the situation where the inviscid flow is fury three-dimensional but is symmetric with respect to the top centre line of the cylinder. The motion of the vortex toward the cylinder lea ds to separation of the boundary layer; in the present work a large un steady adverse pressure gradient develops as well. Results for the thr ee-dimensional streamlines, the vorticity distribution, and the veloci ty component normal to the cylinder indicate the presence of a region of unsteady three-dimensional secondary flow structure of rather compl ex shape located deep within the boundary layer. Within this three-dim ensional secondary flow the fluid is progressively squeezed into a nar row region under the main vortex and it is expected that a local three -dimensional jet will develop sending boundary-layer fluid out into th e main stream. It is pointed out that such three-dimensional eruptive behaviour has been observed in experiments. The results indicate the d evelopment of a three-dimensional singularity in the boundary-layer eq uations.