  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 present the first
formal analytical proof showing that, during the exponential growth of the
instability, the mean (averaged over the disc scale-height) Reynolds stress is
always positive, the mean Maxwell stress is always negative, and hence the mean
total stress is positive and leads to a net outward flux of angular momentum.
More importantly, we show that the ratio of the Maxwell to the Reynolds
stresses during the late times of the exponential growth of the instability is
determined only by the local shear and does not depend on the initial spectrum
of perturbations or the strength of the seed magnetic. 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 this characteristic is qualitatively preserved under more general
conditions, even during the saturated turbulent state generated by the
instability.
