Collision of two vortex rings

Abstract

The interaction of two identical circular viscous vortex rings starting in a side-by-side configuration is investigated by solving the Navier–Stokes equation using a spectral method with 643 grid points. This study covers initial Reynolds numbers (ratio of circulation to viscosity) up to 1153. The vortices undergo two successive reconnections, fusion and fission, as has been visualized experimentally, but the simulation shows topological details not observed in experiments. The shapes of the evolving vortex rings are different for different initial conditions, but the mechanism of the reconnection is explained by bridging (Melander & Hussain 1988) except that the bridges are created on the front of the dipole close to the position of the maximum strain rate. Spatial structures of various field quantities are compared. It is found that domains of high energy dissipation and high enstrophy production overlap, and that they are highly localized in space compared with the regions of concentrated vorticity. The kinetic energy decays according to the same power laws as found in fully developed turbulence, consistent with concentrated regions of energy dissipation. The main vortex cores survive for a relatively long time. On the other hand, the helicity density which is higher in roots of bridges and threads (or legs) changes rapidly in time. The high-helicity-density and high-energy-dissipation regions overlap significantly although their peaks do not always do so. Thus a long-lived structure may carry high-vorticity rather than necessarily high-helicity density. It is shown that the time evolution of concentration of a passive scalar is quite different from that of the vorticity field, confirming our longstanding warning against relying too heavily on flow visualization in laboratory experiments for studying vortex dynamics and coherent structures.