Interaction of an unequal-strength vortex pair

In this investigation, two-dimensional simulations of unequal strength Lamb–Oseen counter-rotating vortex pairs were con-ducted using a spectral-element method. Simulations were per-formed at three different Reynolds numbers, Re = 6660, 13340 and 20000, and various relative strength of vortex circulation ra-tios were considered. The strain adaptation and the viscous re-laxation were shown to be dependent on the relative strength of the vortices, but independent of Reynolds number. The vortex pairs converged to a unique solution on the viscous time-scale for each relative strength value. The completion of the adapta-tion and the relaxation are determined based on the variation of the vortex eccentricity which is a ratio of the strain rate to the vorticity at each vortex center. The viscosity begins to affect the vortex dynamics once those two processes are completed. The two-dimensional simulation results also provide the initial base flows of vortex pairs which will be used in future three-dimensional stability analysis studies