Transition to magnetorotational turbulence in Taylor–Couette flow with imposed azimuthal magnetic field

Abstract

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.

Transport Properties of the Azimuthal Magnetorotational Instability

“…The time discretization is based on the implicit Crank-Nicolson method and is of second order. Details of our numerical method, implementation, and tests can be found in Guseva et al (2015). The numerical resolution was chosen so that our simulations were fully resolved; it reached N=480 finite-difference points in the radial direction and 720 ( =  K 360) and 560 ( =  M 280) Fourier modes in the axial and azimuthal directions.…”

“…For =´-Pm 1.4 10 6 an SW is realized (Guseva et al 2015), whereas at Pm = 1 the AMRI manifests itself as a TW, thereby breaking the axial reflection symmetry (Guseva et al 2017a). Close to Re c the bifurcation is found to be supercritical in all cases.…”

“…We performed direct numerical simulations (DNS) spanning a wide range in Note that Guseva et al (2015Guseva et al ( , 2017a showed that the maximum growth rate of the linear analysis correlates very well with the maximum of the transport for m = 0.26 at low and high Pm. Mamatsashvili et al (2017) have observed the same correlation for the helical MRI.…”

“…Hence, comparing the scaling of G with Re at different Pm and μ is not straightforward. Moreover, Guseva et al (2015Guseva et al ( , 2017a found that at low Pm, close to the Rayleigh line, the turbulence arising from the AMRI is not efficient in transporting momentum. At = -Pm 10 6 and Re  3×10 4 , molecular viscosity is responsible for a significant portion of the momentum transport.…”

Dynamo Action in a Quasi-Keplerian Taylor-Couette Flow

“…In previous work [38][39][40], we considered turbulent Taylor-Couette flows in the presence of an externally imposed azimuthal magnetic field B 0 ðr i =rÞê ϕ , which guarantees the existence of an instability, the so-called azimuthal magnetorotational instability [41,42]. As our finite-amplitude initial condition here, we took a turbulent solution from this work, with Re ¼ Rm ¼ 10 4 .…”