Effects of helicity on the energy transfer in three-dimensional turbulence

Abstract eng:
We investigated the effects of the helicity in the dynamics of the energy transfer in turbulent flows using a modified version of the Navier-Stokes equations with explicit breaking of the mirror symmetry. With an external parameter that controls the imbalance between the number of positive and negative helical Fourier modes we aim to disentangle the role of helicity in the direction of the turbulent energy transfer. In an earlier study with helical projection, an inverse cascade of energy was observed in the three-dimensional Navier-Stokes equations when helicity was maintained sign-definite [1, 2]. In this study we measure the degree to which the parity symmetry controls the direction of the cascade. We introduce a mechanism in which the parity is broken stochastically but in a time frozen manner with helical constraints. We keep triadic interactions in Fourier space involving modes with definite sign of helicity and decimate the triads of other modes with opposite sign of helicity with a fixed probability. We observed a singular behaviour of the direction of the energy cascade measuring a positive forward flux as soon as only a few modes with different helical polarities take part in the dynamics.

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