Viscous diffusion induced evolution of a vortex ring

The evolution of a vortex ring generated by drop impinging on a liquid pool is experimentally, numerically, and analytically investigated. The effect of impingement heights and shapes of the drops on the evolution of the vortex ring are examined in terms of its ring radius, core radius, translational velocity, vorticity, and circulation. We develop a novel analytical model for a finite vortex core to study its evolution in terms of the aforementioned parameters. We verify the proposed model and compare the other existing models with the corresponding experimental results obtained from the drop impingement method. The mathematical model is suitable for predicting both short-time and long-time behavior of the vortex ring in a unified manner. The analytical study unveils the controlling parameters that govern the viscous diffusion-driven evolution of the vortex ring. The circulation dynamics of the ring for the drop impingement method, which has received very little attention, is also experimentally investigated. The Lagrangian particle tracking method is used to study the circulation dynamics of the vortex ring. The combined study of experimental and numerical results, in conjunction with the analytical approach, provides useful insights into the formation of the vortex ring and its viscous diffusion process.