On the Formation of Vortex Pairs near Orifices

It is pointed out that a two-dimensional vortex pair is commonly generated by pushing fluid down a semiinfinite channel by means of an impulsively started piston. Sheffield (1977) calculated the trajecotories of an ideal vortex pair near channel openings of different shapes. The present investigation is concerned with a point-vortex model of the process of pair formation and a general extension of Sheffield's results. The assumption is made that viscous effects are significant only during the separation process and have negligible influence on the overall flow. In the limit of infinite Reynolds number, the problem becomes one of inviscid flow. The growing vortex sheets shed from the edge are represented by a simplified model reported by Brown and Michael (1954). The model is utilized to study the trajectories of two free vortices released symmetrically near the channel wall far from the opening of a semiinfinite channel when growing secondary vortices are present.