title: 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 nonhelical 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 nonhelical turbulence, to a non-Kolmogorov scaling law k^{-7/3} for a maximally helical turbulence. In the latter 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 analyze 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, however, is 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.
authors.affiliation: Université Grenoble Alpes, CNRS, LEGI, Grenoble, France.
authors.forename: Mouloud
authors.initials: M
authors.lastname: Kessar
authors.affiliation: Université Grenoble Alpes, CNRS, ISTerre, Grenoble, France.
authors.forename: Franck
authors.initials: F
authors.lastname: Plunian
authors.affiliation: Institute of Continuous Media Mechanics, Korolyov str. 1, 614013 Perm, Russia.|Perm National Research Polytechnic University, Komsomolskii av. 29, 614990 Perm, Russia.
authors.forename: Rodion
authors.initials: R
authors.lastname: Stepanov
authors.affiliation: Université Grenoble Alpes, CNRS, LEGI, Grenoble, France.
authors.forename: Guillaume
authors.initials: G
authors.lastname: Balarac