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.
Bibliographical noteFunding Information:
R.O.M. thanks the Core facility for Advanced Computing and Data Science (CACDS) at the University of Houston for providing computing resources. Funding: This research was funded by the National Science Foundation through the Harvard Materials Research Science and Engineering Center DMR-1420570 and through the Division of Mathematical Sciences DMS-1411694 and DMS-1715477. M.P.B. is an investigator of the Simons Foundation. A.P. acknowledges financial support from the IDEXLYON project (Contract ANR-16-IDEX-0005) under
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