The magnetorotational instability (MRI) is thought to be a powerful source of turbulence and momentum transport in astrophysical accretion discs, but obtaining observational evidence of its operation is challenging. Recently, laboratory experiments of Taylor-Couette flow with externally imposed axial and azimuthal magnetic fields have revealed the kinematic and dynamic properties of the MRI close to the instability onset. While good agreement was found with linear stability analyses, little is known about the transition to turbulence and transport properties of the MRI.We here report on a numerical investigation of the MRI with an imposed azimuthal magnetic field. We show that the laminar Taylor-Couette flow becomes unstable to a wave rotating in the azimuthal direction and standing in the axial direction via a supercritical Hopf bifurcation. Subsequently, the flow features a catastrophic transition to spatio-temporal defects which is mediated by a subcritical subharmonic Hopf bifurcation. Our results are in qualitative agreement with the PROMISE experiment and dramatically extend their realizable parameter range. We find that as the Reynolds number increases defects accumulate and grow into turbulence, yet the momentum transport scales weakly.

We numerically compute the flow of an electrically conducting fluid in a Taylor-Couette geometry where the rotation rates of the inner and outer cylinders satisfy Ω o =Ω i ¼ ðr o =r i Þ −3=2 . In this quasi-Keplerian regime, a nonmagnetic system would be Rayleigh stable for all Reynolds numbers Re, and the resulting purely azimuthal flow incapable of kinematic dynamo action for all magnetic Reynolds numbers Rm. For Re ¼ 10 4 and Rm ¼ 10 5 , we demonstrate the existence of a finite-amplitude dynamo, whereby a suitable initial condition yields mutually sustaining turbulence and magnetic fields, even though neither could exist without the other. This dynamo solution results in significantly increased outward angular momentum transport, with the bulk of the transport being by Maxwell rather than Reynolds stresses.

The magnetorotational instability (MRI) is thought to be a powerful source of turbulence in Keplerian accretion disks. Motivated by recent laboratory experiments, we study the MRI driven by an azimuthal magnetic field in an electrically conducting fluid sheared between two concentric rotating cylinders. By adjusting the rotation rates of the cylinders, we approximate angular velocity profiles w µ r q . We perform direct numerical simulations of a steep profile close to the Rayleigh line  -q 2 and a quasi-Keplerian profile » -q 3 2 and cover wide ranges of Reynolds ( Ŕe 4 10 4 ) and magnetic Prandtl numbers (   0 Pm 1). In the quasi-Keplerian case, the onset of instability depends on the magnetic Reynolds number, with » Rm 50 c , and angular momentum transport scales as Pm Re 2 in the turbulent regime. The ratio of Maxwell to Reynolds stresses is set by Rm. At the onset of instability both stresses have similar magnitude, whereas the Reynolds stress vanishes or becomes even negative as Rm increases. For the profile close to the Rayleigh line, the instability shares these properties as long as 