  We develop a local model for the exponential growth and saturation of the
Reynolds and Maxwell stresses in turbulent flows driven by the
magnetorotational instability. We first derive equations that describe the
effects of the instability on the growth and pumping of the stresses. We
highlight the relevance of a new type of correlations that couples the
dynamical evolution of the Reynolds and Maxwell stresses and plays a key role
in developing and sustaining the magnetorotational turbulence. We then
supplement these equations with a phenomenological description of the triple
correlations that lead to a saturated turbulent state. We show that the
steady-state limit of the model describes successfully the correlations among
stresses found in numerical simulations of shearing boxes.
