Ring vortex collisions and the turbulent cascade

A research question I started during my post-doc is the simulation of the head-on collision of two ring vortices, to study the turbulent cascade. Two counter-rotating rings colliding head-on disintegrate into smoke in a matter of milliseconds, providing a canonical system for studying the fast formation of minute (turbulent) structures from relatively smooth initial conditions. Experiments find it hard to measure everything that is going on, but simulations have a hard time figuring out which are the correct initial conditions to use: very smooth initial conditions can produce very different physics to conditions with a degree of noise.

High-speed visualization techniques have provided us with a new method to study these collisions. In this video, submitted to the Gallery of Fluid Motion, we can see indications of a mechanism similar to a turbulent cascade appearing, which transfers energy across scales. During several years, we worked to characterize the system both experimentally and numerically, and related it to the interaction between counter-rotating vortex tubes. We found evidence of iterative instabilities, and related those to the energy transfer in turbulence, finding that vortex tubes and rings were not a good model of the turbulent cascade. During the process, we characterized the development of instabilities in vortex rings when they interact with each other, or with walls and free-slip surfaces. We also studied the interaction of vortex tubes at different angles, finding regions where vortex reconnection or iterative instabilities dominate.

As a final side-project, we investigated the effect of a magnetic field on vortex-tube interaction, due to the relevance of this process in the formation of sunspots. This led to a manuscript, and a second award-winning video where we separated different regimes of magnetically and vorticity dominated interactions, finding that vortices with a strong magnetic field tend to be very stable in situations where they would normally disintegrate.