Numerical Simulations of Two Coaxial Vortex Rings Head-on Collision (Advances in Applied Mathematics and Mechanics, 2018)
Vortex rings have been a subject of interest in vortex dynamics due to aplethora of physical phenomena revealed by their motions and interactions withina boundary. The present paper is devoted to physics of a head-on collision of twovortex rings in three dimensional space, simulated with a second order finite volumescheme and compressible. The scheme combines non-iterative approximate Riemann-solverand piecewise-parabolic reconstruction used in inviscid flux evaluation procedure.The computational results of vortex ring collisions capture several distinctivephenomena. In the early stages of the simulation, the rings propagate under their ownself-induced motion. As the rings approach each other, their radii increase, followedby stretching and merging during the collision. Later, the two rings have merged intoa single doughnut-shaped structure. This structure continues to extend in the radialdirection, leaving a web of particles around the centers. At a later time, the formationof ringlets propagate radially away from the center of collision, and then the effects ofinstability involved leads to a reconnection in which small-scale ringlets are generated.In addition, it is shown that the scheme captures several experimentally observedfeatures of the ring collisions, including a turbulent breakdown into small-scale structuresand the generation of small-scale radially propagating vortex rings, due to themodification of the vorticity distribution, as a result of the entrainment of backgroundvorticity and helicity by the vortex core, and their subsequent interaction.