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.

International audienceIn this work, the accuracy of various models used in large-eddy simulations (LES) of incompressible magnetohydrodynamic (MHD) turbulence is evaluated. Particular attention is devoted to the capabilities of models to reproduce the transfers between resolved grid- and subgrid-scales. The exact global balance of MHD turbulent flows is first evaluated from direct numerical simulation (DNS) database. This balance is controlled by the transfers between scales and between kinetic and magnetic energies. Two cases of forced homogeneous isotropic MHD turbulent flows are considered, with and without injecting large scale helicity. The strong helical case leads to domination of the magnetic energy due to an inverse cas- cade [A. Brandenburg, Astrophys. J. 550(2), 824 (2001); N. E. Haugen et al., Phys. Rev. E 70(1), 016308 (2004)]. The energy transfers predicted by various models are then compared with the transfer extracted from DNS results. This allows to discriminate models classically used for LES of MHD turbulence. In the non-helical case, the Smagorinsky-like model [M. L. Theobald et al., Phys. Plasmas 1, 3016 (1994)] and a mixed model are able to perform stable LES, but the helical case is a more demanding test and all the models lead to unstable simulations