Discontinuous Transition from Direct to Inverse Cascade in Three-Dimensional Turbulence

Ganapati Sahoo, Alexandros Alexakis, and Luca Biferale
Phys. Rev. Lett. 118, 164501 – Published 17 April 2017

Abstract

Inviscid invariants of flow equations are crucial in determining the direction of the turbulent energy cascade. In this work we investigate a variant of the three-dimensional Navier-Stokes equations that shares exactly the same ideal invariants (energy and helicity) and the same symmetries (under rotations, reflections, and scale transforms) as the original equations. It is demonstrated that the examined system displays a change in the direction of the energy cascade when varying the value of a free parameter which controls the relative weights of the triadic interactions between different helical Fourier modes. The transition from a forward to inverse cascade is shown to occur at a critical point in a discontinuous manner with diverging fluctuations close to criticality. Our work thus supports the observation that purely isotropic and three-dimensional flow configurations can support inverse energy transfer when interactions are altered and that inside all turbulent flows there is a competition among forward and backward transfer mechanisms which might lead to multiple energy-containing turbulent states.

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  • Received 25 January 2017

DOI:https://doi.org/10.1103/PhysRevLett.118.164501

© 2017 American Physical Society

Physics Subject Headings (PhySH)

  1. Research Areas
Fluid Dynamics

Authors & Affiliations

Ganapati Sahoo1, Alexandros Alexakis2, and Luca Biferale1

  • 1Department of Physics and INFN, University of Rome ‘Tor Vergata,’ Via della Ricerca Scientifica 1, 00133 Rome, Italy
  • 2Laboratoire de Physique Statistique, École Normale Supérieure, CNRS, Université Pierre et Marié Curie, Université Paris Diderot, 24 rue Lhomond, 75005 Paris, France

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Issue

Vol. 118, Iss. 16 — 21 April 2017

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