Sinusoidal flow around a circular cylinder

In this investigation, the flow around a stationary cylinder, which is subjected to a sinusoidally varying freestream velocity, was studied analytically. The flow considered was characterized by symmetric vortex pairs which were forcibly shed from the cylinder due to the oscillating nature of the flow. The problem was formulated in terms of inviscid potential flow theory. The physical vortices and the separated boundary layers feeding the vortices were replaced with vortex filaments and vortex sheets using the lumped vortex model. The resulting formulation provided equations which could be solved for the instantaneous locations and strengths of the vortices. A mathematical condition for the forced shedding of the vortices was postulated and after this shedding had occurred, the vortices were treated as free vortices. [...]