Non-Kolmogorov cascade of helicity driven turbulence

Abstract

We solve the Navier-Stokes equations with two simultaneous forcings. One forcing is applied at a given large-scale and it injects energy. The other forcing is applied at all scales belonging to the inertial range and it injects helicity. In this way we can vary the degree of turbulence helicity from non helical to maximally helical. We find that increasing the rate of helicity injection does not change the energy flux. On the other hand the level of total energy is strongly increased and the energy spectrum gets steeper. The energy spectrum spans from a Kolmogorov scaling law $k^{-5/3}$ for a non-helical turbulence, to a non-Kolmogorov scaling law $k^{-7/3}$ for a maximally helical turbulence. In the later case we find that the characteristic time of the turbulence is not the turnover time but a time based on the helicity injection rate. We also analyse the results in terms of helical modes decomposition. For a maximally helical turbulence one type of helical mode is found to be much more energetic than the other one, by several orders of magnitude. The energy cascade of the most energetic type of helical mode results from the sum of two fluxes. One flux is negative and can be understood in terms of a decimated model. This negative flux is however not sufficient to lead an inverse energy cascade. Indeed the other flux involving the least energetic type of helical mode is positive and the largest. The least energetic type of helical mode is then essential and cannot be neglected.

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Cited by in corpus (12)

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• Hindered energy cascade in highly helical isotropic turbulence
• Helically Decomposed Turbulence
• Discontinuous transition from direct to inverse cascade in three-dimensional turbulence
• Variable energy flux in turbulence
• Inverse cascade of energy in helical turbulence
• Effects of magnetic and kinetic helicities on the growth of magnetic fields in laminar and turbulent flows by helical-Fourier decomposition
• Enstrophy transfers in helical turbulence
• Helicoidal particles in turbulent flows with multi-scale helical injection
• New Exact Betchov-like Relation for the Helicity Flux in Homogeneous Turbulence
• A self-induced mechanism of large-scale helical structures in compressible turbulent flows
• A mass-, kinetic energy- and helicity-conserving mimetic dual-field discretization for three-dimensional incompressible Navier-Stokes equations, part I: Periodic domains