  In the present note, we solved numerically the viscous vorticity equation of
the initial-boundary value problem describing the classic Helmholtz phenomena
of vortex interaction. In the leapfrogging of vortex pairs, we demonstrate the
fact that there exists a variety of initial vortex configurations, such as the
initial vortex core structures, the starting speeds, the lateral and
longitudinal separations as well as the fluid viscosity. To simulate
leapfrogging appears to be a straightforward task, based on the vorticity
calculations for a number of initial vortices with different core structures.
Indeed, the evaluation of the unsteady vortex interactions requires accurate
numerical simulations, and the solutions are diverse and intriguing. In
particular, the impact of two asymmetric approaching vortices can produce
peeled-off fission vortices or cross-bred eddies of mushroom topology. Over the
course of flow development, we are unable to define any unique consistent
Reynolds number which may be used to classify the individual flows, because of
the multiplicity of characteristic lengths and velocity scales. Our key
observation is that the initial-boundary value problems of fluid motion do not
necessarily imply the realization of dynamically similar flows.
