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.

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Cited by in corpus (21)

• The Openpipeflow Navier--Stokes Solver
• Stability and instability of hydromagnetic Taylor-Couette flows
• Metal pad instabilities in liquid metal batteries
• Dynamo Action in a Quasi-Keplerian Taylor-Couette Flow
• Phase-field simulation of core-annular pipe flow
• nsCouette -- A high-performance code for direct numerical simulations of turbulent Taylor-Couette flow
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• Generalised quasi-linear approximation of the HMRI
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• A systematic route to subcritical dynamo branches
• Analysis and modeling of localized invariant solutions in pipe flow
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• The origin of localized snakes-and-ladders solutions of plane Couette flow
• Nonaxisymmetric MHD instabilities of Chandrasekhar states in Taylor-Couette geometry
• Analysis of azimuthal magnetorotational instability of rotating MHD flows and Tayler instability via an extended Hain-Lust equation
• Transition to chaos and modal structure of magnetized Taylor-Couette flow
• Absolute versus convective helical magnetorotational instabilities in Taylor-Couette flows
• Taylor rolls on tour: Slow drift of turbulent large-scale structures in flows with continuous symmetries
• Centrifugal instability of Taylor-Couette flow in stratified and diffusive fluids