A method to control and analyze vortex ring collisions in the laminar regime

Head-on symmetrical collisions between two vortex rings can lead to a reconnection of vortex filaments and, via energy flow, a divergent cascade of smaller and larger secondary rings. How these complex collisions distribute energy over time to produce diverse secondary rings is mysterious. Experimental physicists at the University of Chile address this question and report their findings in Physics of Fluids.

The authors formulated their research problem both experimentally and numerically using a vortex generation method. Using a generation chamber with height Lz = 20D₀, they secured the natural development of the vorticity structures in the z dimension perpendicular to the collision plane.

Together, the mass conservation equation and Navier Stokes equation for momentum conservation governed their problem, which the researchers solved numerically in the laminar regime for an incompressible Newtonian fluid without the influence of gravity.

The authors used numerical simulation to produce stunning imagery of collisions between three- (3R) and six- (6R) secondary laminar vortex ring structures in free fight and they measured the vortex rings’ velocity, pressure, and vorticity fields. They verified, experimentally, the resulting secondary vortex structures in the 3R situation.

The authors observed the formation of two secondary vortex rings from the 3R and 6R collisions which achieved a rapid radial expansion a split second after the collision. They also discovered that the larger the Reynolds number (Re < 10³), the greater the vortex ring speed across the z-axis. In the 6R collision case, the ring diameter increased linearly and up to twice as large as those in the 3R collision case.

Moving forward, lead-author Rodrigo Hernandez states that although controlled collisions between many rings remain challenging, these controlled collisions are a seminal platform for future research.

Source: “Symmetrical collision of multiple vortex rings,” by R. H. Hernández and T. Reyes, Physics of Fluids (2017). The article can be accessed at https://doi.org/10.1063/1.5004587 .