On the roles of antisymmetric vorticity and particles changing over in two-dimensional vortex merging problems

Abstract

The two-dimensional vortex merging problem has been solved for a wide range of ReΓ values and for inviscid media. Accurate numerical solutions from a spectral method on 1024 × 1024 grids are utilized to report new findings on the mechanisms involved in different stages of merging. We have identified the role of the antisymmetric part of vorticity in causing the alternating nature of radial movement of the vortices, thus explaining the mechanism for oscillations in the variation of the separation distance in stage-3. Alternations of radial velocity place a limit on the rate of reduction of the separation distance by convection during the final phase of merging. As another major contribution of the present work, we have reported the role of viscosity in smooth and fast merging of the vortices through a process called “particles changing over.” This is true for the investigated inviscid case also, wherein the hyper-viscosity included for stabilization of the numerical solution performs the process of particles changing over. The vortex merging in stage-3 of two-dimensional vortex interactions is an “alternating convection and particles changing over phase.”