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 an iterative cascade of instabilities in a bulk fluid. When the coherent vortex cores approach each other, they deform into tentlike 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 mechanistic framework in which the evolution of turbulent flows can be examined in real time as a series of discrete dynamic instabilities.
Bibliographical noteFunding Information:
This research was funded by the National Science Foundation through the Harvard Materials Research Science and Engineering Center Grant No. DMR-1420570 and through Division of Mathematical Sciences Grants No. DMS-1411694 and No. DMS-1715477. S.M.R. acknowledges support from the Alfred P. Sloan Foundation. A.P. received support from the IDEXLyon project (Contract No. ANR-16-IDEX-0005) under University of Lyon auspices.
© 2018 American Physical Society.