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Cascade leading to the emergence of small structures in vortex ring collisions

Ryan McKeown (1), Rodolfo Ostilla-Mónico (1)(2), Alain Pumir (3), Michael P. Brenner (1), and Shmuel M. Rubinstein (1)

Physical Review Fluids, 3, Issue 12, 17 December 2018. DOI:10.1103/PhysRevFluids.3.124702


Vortex ring collision; Fluid dynamics; Turbulence; Image analysis


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…

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Author Affiliation

(1) School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
(2) Department of Mechanical Engineering, University of Houston, Houston, Texas 77204, USA
(3) Université de Lyon, Laboratoire de Physique, ENS de Lyon, Université Claude Bernard, CNRS, 69342 Lyon, France

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