Reynolds Number Effects on Vortex Merging Criterion

Asymmetric vortex pair interactions are effectively characterized by a mutuality parameter, $MP=S_1/S_2$, which compares the relative straining, $S_i=s_i/w_i$, experienced by each vortex (Folz and Nomura, JFM 2017). When $S_1$ and $S_2$ are comparable, $MP\approx 1$, a two-way interaction ensues: both vortices undergo core detrainment ($S_i>S_c_r$), which enables a mutual entrainment process to form a compound vortex. As relative straining becomes more disparate, mutuality is diminished until $MP>MP_c_r$, and the interaction is one-way: one vortex detrains and is destroyed by the other, which remains unaffected. The value of the merging criterion, $MP_c_r$, differed for the values of Re = 1000 and 5000 considered. In this study, a range of $Re=250$ to 50000 is investigated using numerical simulations. Three flow regimes are identified: when $Re<500$, diffusion dominates, and in the absence of convection, $MP_c_r$ is not observed; when $5005000$, convection dominates and $MP_c_r$ is independent of $Re$. These results provide insight to more complicated flows, such a 2D turbulence, which are driven by asymmetric vortex interactions occurring over a range of $Re$.