A Cascade Leading to the Emergence of Small Structures in Vortex Ring Collisions

TL;DR

This paper demonstrates experimentally and numerically that vortex ring collisions at high Reynolds numbers produce a novel iterative cascade of instabilities, leading to turbulence and small-scale structures in fluid flows.

Contribution

It uncovers a new iterative cascade mechanism of vortex instabilities during vortex ring collisions, supported by experimental evidence and Navier-Stokes simulations.

Findings

Observation of vortex core deformation into tent-like structures

Identification of a cascade of vortex sheet breakups into smaller filaments

Numerical resolution of one iteration of the instability cascade

Abstract

When vortex rings collide head-on at high enough Reynolds numbers, they ultimately annihilate through a violent interaction which breaks down their cores into a turbulent cloud. We experimentally show that this very strong interaction, which leads to the production of fluid motion at very fine scales, uncovers direct evidence of a novel iterative cascade of instabilities in a bulk fluid. When the coherent vortex cores approach each other, they deform into tent-like structures, and the mutual strain causes them to locally flatten into extremely thin vortex sheets. These sheets then break down into smaller secondary vortex filaments, which themselves rapidly flatten and break down into even smaller tertiary filaments. By performing numerical simulations of the full Navier-Stokes equations, we also resolve one iteration of this instability and highlight the subtle role that viscosity must play in the rupturing of a vortex sheet. The concurrence of this observed iterative cascade of instabilities over various scales with those of recent theoretical predictions could provide a new mechanistic framework in which the evolution of turbulent flows can be examined in real-time as a series of discrete dynamic instabilities.