The influence of collision angle for viscous vortex reconnection

Abstract

We revisit the mechanism of viscous vortex reconnection by considering the collision of vortex rings over a range of initial collision angles and Reynolds numbers. While the overall reconnection process is similar to anti-parallel vortex reconnection, we find that collision angle exerts significant influence over the process, altering the evolution of various global and local quantities. The collision angle primarily manipulates the "pyramid"process, a recently identified stretching mechanism proposed by Moffatt and Kimura ["Towards a finite-time singularity of the Navier-Stokes equations Part 1. Derivation and analysis of dynamical system,"J. Fluid Mech., 861, 930-967 (2019)] to be a potential pathway for finite-time singularity of Euler's equations, during the approach stage of the rings. However, the "pyramid"process is short-lived for viscous vortices. The present work shows that the "pyramid"process is arrested by parallelization of the colliding vortices, wherein contact of the colliding vortices halts their motion toward each other at the pyramid apex, allowing the rest of the vortex tube to "catch up,"breaking the pyramid structure. Parallelization marks the transition to a second phase of stretching, where the colliding vortices remain parallel. Vorticity amplification from pyramid stretching is significantly stronger than for its parallel counterpart, and is thus the dominant factor determining reconnection properties. Based upon the findings in this study, we conjecture that the parallelization process is the primary mechanism that prevents the finite-time singularity through the pyramid process. Critically, the Reynolds number scaling for the reconnection rate differs depending on the collision angle, which challenges the conjecture of universal Reynolds number scaling in the literature.