  We study the development of coherent structures in local simulations of the
magnetorotational instability in accretion discs in regimes of on-off
intermittency. In a previous paper [Chian et al., Phys. Rev. Lett. 104, 254102
(2010)], we have shown that the laminar and bursty states due to the on-off
spatiotemporal intermittency in a one-dimensional model of nonlinear waves
correspond, respectively, to nonattracting coherent structures with higher and
lower degrees of amplitude-phase synchronization. In this paper we extend these
results to a three-dimensional model of magnetized Keplerian shear flows.
Keeping the kinetic Reynolds number and the magnetic Prandtl number fixed, we
investigate two different intermittent regimes by varying the plasma beta
parameter. The first regime is characterized by turbulent patterns interrupted
by the recurrent emergence of a large-scale coherent structure known as
two-channel flow, where the state of the system can be described by a single
Fourier mode. The second regime is dominated by the turbulence with sporadic
emergence of coherent structures with shapes that are reminiscent of a
perturbed channel flow. By computing the Fourier power and phase spectral
entropies in three-dimensions, we show that the large-scale coherent structures
are characterized by a high degree of amplitude-phase synchronization.
