A quantitative assessment of viscous asymmetric vortex pair interactions

The interactions of two like-signed vortices in viscous fluid are investigated using two-dimensional numerical simulations performed across a range of vortex strength ratios, , corresponding to vortices of circulation, , with differing initial size and/or peak vorticity. In all cases, the vortices evolve by viscous diffusion before undergoing a primary convective interaction, which ultimately results in a single vortex. The post-interaction vortex is quantitatively evaluated in terms of an enhancement factor, , which compares its circulation, , to that of the stronger starting vortex, . Results are effectively characterized by a mutuality parameter, , where the ratio of induced strain rate, , to peak vorticity, , for each vortex, , is found to have a critical value, , above which core detrainment occurs. If is sufficiently close to unity, both vortices detrain and a two-way mutual entrainment process leads to , i.e. merger. In asymmetric interactions and mergers, generally one vortex dominates; the weak/no/strong vortex winner regimes correspond to , respectively. As deviates from unity, decreases until a critical value, is reached, beyond which there is only a one-way interaction; one vortex detrains and is destroyed by the other, which dominates and survives. There is no entrainment and , i.e. only a straining out occurs. Although appears to be independent of Reynolds number, shows a dependence. Comparisons are made with available experimental data from Meunier (2001, PhD thesis, Universite de Provence-Aix-Marseille I).