Leapfrogging criteria for a line vortex pair external to a circular cylinder

The interaction of two line vortices of differing strengths in the presence of a circular cylinder is considered. Explicit criteria are derived, a function of vortex strengths (including strengths of opposite signs) and the cylinder radius, which separate different behaviors of the system. If the initial position of the vortices satisfies these criteria, they will undergo a periodic leapfrogging motion as they rotate around the cylinder; otherwise, the vortices still interact weakly with one another except without leapfrogging. This is in contrast to the planar wall case where if no periodic leapfrogging occurs, the vortices move apart and do not interact with each other. Numerical results for initial vortex positions which do and do not satisfy these criteria are presented to demonstrate the different motions available, as well as the robustness of the criteria. Published under license by AIP Publishing.