Turbulence generation through an iterative cascade of the elliptical instability

February 28, 2020

Ryan McKeown (1), Rodolfo Ostilla-Mónico (2), Alain Pumir (3), Michael P. Brenner(1), Shmuel M. Rubinstein (1)
Science Advances, 6, Issue 9, February 2020. DOI: 10.1126/sciadv.aaz2717


The essence of turbulent flow is the conveyance of energy through the formation, interaction, and destruction of eddies over a wide range of spatial scales—from the largest scales where energy is injected down to the smallest scales where it is dissipated through viscosity. Currently, there is no mechanistic framework that captures how the interactions of vortices drive this cascade. We show that iterations of the elliptical instability, arising from the interactions between counter-rotating vortices, lead to the emergence of turbulence. We demonstrate how the nonlinear development of the elliptical instability generates an ordered array of antiparallel secondary filaments. The secondary filaments mutually interact, leading to the formation of even smaller tertiary filaments. In experiments and simulations, we observe two and three iterations of this cascade, respectively. Our observations indicate that the elliptical instability could be one of the fundamental mechanisms by which the turbulent cascade develops.

How Our Software Was Used

Dragonfly was used to reconstruct a series of volumetric scans, in full 3D with temporal evolution, of two vortex rings colliding.

Author Affiliation

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