A two-dimensional vortex pair is commonly generated by pushing fluid down a semi-infinite channel by means of an impulsively started piston. The strength and separation of the two fully developed vortices strongly depend upon the time history of the piston motion. When the piston is impulsively stopped, two secondary vortices are formed downstream of the channel ends and interact with the primary pair in a fairly complicated way.
In the present work we attempt to provide a discrete-vortex model of the process of pair formation. The effects of viscosity are assumed to affect only the separation process, having negligible influence on the overall flow. In the limit of infinite Reynolds number, the problem becomes one of inviscid flow, and the separation at the sharp edges is approximated by a Kutta–Joukowski condition, large vortex regions being replaced by simple concentrated vortices. The growing vortex sheets shed from the edge are represented by a simplified model due to Brown and Michael.
Present results are able to account for the failure of the ‘puffing’ technique as well as the success of Barker and Crow's ‘downwash’ technique in producing vortex pairs.
Flow-visualization experiments are also reported, and good qualitative agreement is found between numerical and experimental results.
The present model also shows that the presence of secondary vortices drastically modifies the trajectories of free vortices as obtained in a previous work due to Sheffield.