Quantifying the reconnection process of two vortices

In this work, we use DNS to study the reconnection of two vortices. The Navier-Stokes equations are solved using a Fourier pseudospectral algorithm with triply periodic boundary conditions. The zero-circulation constraint, which was found to be problematic by Pradeep \& Hussain (2004), is circumvented by solving the governing equations in a proper rotating frame. To quantify the reconnection of two vortices, an approach using vortex filaments is considered. This approach is first validated against the results of Hussain \& Duraisamy (2011) for two parallel counter-rotating vortices. In this latter case, symmetries in the initial flow provide a simple way to compute the instantaneous rate of reconnection. Next, we study the interaction of orthogonal, unequal strength vortices for which only partial reconnection can occur. Typically, the weak vortex ($\Gamma_2$) is seen to deform and wrap itself around the strong one ($\Gamma_1$) to (partially) reconnect. For Reynolds numbers ($\Gamma_1/\nu$) of the order of $10^3$ and circulation ratios $0.1\leq\Gamma_2/\Gamma_1\leq0.9$, we compute the instantaneous reconnection rate and observe the propagating vorticity structures. Particularly, we look at some of the topological features that can be well visualized with vortex filaments.