Non-linear energy transfers in accretion discs MRI turbulence I. Net vertical field case

The magnetorotational instability (MRI) is believed to be responsible for most of the angular momentum transport in accretion discs. However, molecular dissipation processes may drastically change the efficiency of MRI turbulence in realistic astrophysical situations. The physical origin of this dependency is still poorly understood as linear and quasi linear theories fail to explain it. In this paper, we look for the link between molecular dissipation processes and MRI transport of angular momentum in unstratified shearing box simulations, including a mean vertical field. We show that magnetic helicity is unimportant in the model we consider. We perform a spectral analysis on the simulations tracking energy exchanges in spectral space when turbulence is fully developed. We find that the energy exchanges are essentially direct (from large to small scale) whereas some non-linear interactions appear to be non-local in spectral space. We speculate that these non-local interactions are responsible for the correlation between turbulent transport and molecular dissipation. We argue that this correlation should then disappear when a significant scale separation is achieved, and we discuss several methods by which one can test this hypothesis.