The signature of the magnetorotational instability in the Reynolds and Maxwell stress tensors in accretion discs

The magnetorotational instability is thought to be responsible for the generation of magnetohydrodynamic turbulence that leads to enhanced outward angular momentum transport in accretion discs. Here, we demonstrate that, during the exponential growth of the instability, the mean Reynolds stress is always positive, the mean Maxwell stress is always negative, and hence the total stress is positive and leads to a net outward angular momentum flux. More importantly, we show that the ratio of the Maxwell to the Reynolds stresses at late times is determined only by the local shear and does not depend on the initial spectrum of perturbations or the strength of the seed magnetic field. Even though we derived these properties of the stress tensors for the exponential growth of the instability in incompressible flows, numerical simulations of shearing boxes show that they are preserved under more general conditions, even during the saturated state of the turbulence generated by the instability.