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Abstract

The head-on collision of two vortex rings can produce diverse phenomena: A tiara of
secondary rings, vortex sheets which flatten and interact iteratively, or the violent disintegration of the rings into a turbulent cloud. The outcome of the interaction is determined
by the nature of the instability affecting two impinging vortex rings. Here we carry out a
systematic study to determine the dominant instability as a function of the parameters of
the problem. To this end, we numerically simulate the head-on collision of vortex rings
with circulation Reynolds numbers between 1000 and 3500 and varying slenderness ratios
L = a/R ranging from L = 0.1 to 0.35, with a the core radius and R the ring radius. By
studying the temporal evolution of the energy and viscous dissipation, we elucidate the role
azimuthal instabilities play in determining what the outcomes of the collision are. We then
compare these collisions to the head-on impact of a vortex ring on a free-slip and a no-slip
wall. The free-slip wall imposes a mirror symmetry, which impedes certain instabilities
and at sufficiently large Reynolds numbers leads to the formation of a half-tiara of vortices.
Impact against a no-slip wall results in the process where a secondary vortex ring is formed
after the ejection of the resulting boundary layer. When the Reynolds number is above
a certain threshold, which increases with , the vortices disintegrate through azimuthal
instabilities, resulting in a turbulent cloud.