Eur. Phys. J. E (2015) 38: 114
https://doi.org/10.1140/epje/i2015-15114-4

Regular Article

Disentangling the triadic interactions in Navier-Stokes equations

Department of Physics and INFN, University of Rome “Tor Vergata”, Via della Ricerca Scientifica 1, 00133, Rome, Italy

^* e-mail: ganapati.sahoo@gmail.com

Received: 21 September 2015
Revised: 13 October 2015
Accepted: 15 October 2015
Published online: 30 October 2015

Abstract

We study the role of helicity in the dynamics of energy transfer in a modified version of the Navier-Stokes equations with explicit breaking of the mirror symmetry. We select different set of triads participating in the dynamics on the basis of their helicity content. In particular, we remove the negative helically polarized Fourier modes at all wave numbers except for those falling on a localized shell of wave number, . Changing k_m to be above or below the forcing scale, k_f, we are able to assess the energy transfer of triads belonging to different interaction classes. We observe that when the negative helical modes are present only at a wave number smaller than the forced wave numbers, an inverse energy cascade develops with an accumulation of energy on a stationary helical condensate. Vice versa, when negative helical modes are present only at a wave number larger than the forced wave numbers, a transition from backward to forward energy transfer is observed in the regime when the minority modes become energetic enough.