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, [STIX]x1D6EC=[STIX]x1D6E4₁/[STIX]x1D6E4₂ 1 , corresponding to vortices of circulation, [STIX]x1D6E4ᵢ , 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, [STIX]x1D700=[STIX]x1D6E4end/[STIX]x1D6E42,start , which compares its circulation, [STIX]x1D6E4end , to that of the stronger starting vortex, [STIX]x1D6E42,start . Results are effectively characterized by a mutuality parameter, MP≡ (S/[STIX]x1D714)₁/(S/[STIX]x1D714)₂ , where the ratio of induced strain rate, S , to peak vorticity, [STIX]x1D714 , for each vortex, (S/[STIX]x1D714)ᵢ , is found to have a critical value, (S/[STIX]x1D714)cr≈ 0.135 , above which core detrainment occurs. If $MP$ is sufficiently close to unity, both vortices detrain and a two-way mutual entrainment process leads to [STIX]x1D700>1 , i.e. merger. In asymmetric interactions and mergers, generally one vortex dominates; the weak/no/strong vortex winner regimes correspond to $MP<,=,>1$ , respectively. As $MP$ deviates from unity, [STIX]x1D700 decreases until a critical value, MPcr 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 [STIX]x1D700~ 1 , i.e. only a straining out occurs. Although (S/[STIX]x1D714)cr appears to be independent of Reynolds number, MPcr shows a dependence. Comparisons are made with available experimental data from Meunier (2001, PhD thesis, Université de Provence-Aix-Marseille I).