Vortex tube reconnection at Re = 10⁴

We present simulations of the long-time dynamics of two anti-parallel vortex tubes with and without initial axial flow, at Reynolds number Re = Γ/v = 10⁴. Simulations were performed in a periodic domain with a remeshed vortex method using 785 × 10⁶ particles. We quantify the vortex dynamics of the primary vortex reconnection that leads to the formation of elliptical rings with axial flow and report for the first time a subsequent collision of these rings. In the absence of initial axial flow, a -5/3 slope of the energy spectrum is observed during the first reconnection of the tubes. The resulting elliptical vortex rings experience a coiling of their vortex lines imparting an axial flow inside their cores. These rings eventually collide, exhibiting a -7/3 slope of the energy spectrum. Studies of vortex reconnection with an initial axial flow exhibit also the -7/3 slope during the initial collision as well as in the subsequent collision of the ensuing elliptical vortex rings. We quantify the detailed vortex dynamics of these collisions and examine the role of axial flow in the breakup of vortex structures.