Dynamics and transport of magnetorotational instabilities in Taylor--Couette flows
Astrophysics and Astronomy
Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics
Final Report Abstract
The aim of the present project was the detailed investigation of the nonlinear properties of the magnetorotational instability in Taylor–Couette flows by means of direct numerical simulations. Overall, a comprehensive understanding of the instabilities, transition to turbulence and subsequent enhancement of angular momentum transport, with focus mostly on azimuthal magnetic fields, was obtained. The main results can be summarized as follows: • At low magnetic Prandtl number P m the azimuthal magnetorotational instability (AMRI) manifests itself as a wave rotating in the azimuthal direction and standing in the axial direction, thereby preserving the reflection symmetry in the latter. As the Reynolds number Re increases, a catastrophic transition to spatio-temporal chaos occurs. In a wide range of parameters, the standing wave and the chaotic flow are both locally stable and can be realized depending on the initial conditions. We found that the first step in this transition process is a subcritical Hopf bifurcation giving rise to an unstable relative periodic orbit, which consists of a long-wave modulation of the axially periodic pattern of the standing wave and destroys the homogeneity of the vortical pattern. It can thus be seen as a temporally simple defect precursor of the ensuing spatio-temporal chaos. Our numerical results were found in good agreement with the PROMISE experiments. • At large Pm the AMRI arises as either a standing or a traveling wave, with the latter being a spontaneous breaking of the axial reflection symmetry of the system. Overall, the bifurcation scenario at large Pm is richer and involves spatially complex, but temporally periodic, stable structures. In both low and high Pm cases, accumulation of spatial defects results in turbulence. • The dependence of the angular momentum transport on the Reynolds and magnetic Prantdl numbers was computed and analyzed (approaching the asymptotic scaling regimes). It was found that AMRI turbulence can transport angular momentum efficiently, at least for high Pm (as in highly ionized accretion disks). Two flow regimes with different mechanisms of momentum transport were identified and analyzed: inertial and magnetocoriolis waves, with a crossover at magnetic Reynolds number Rm ≈ 100. • A small-scale self-generated and self-sustained dynamo operating in Rayleigh-stable flows was observed for Pm = 10 and Rm = 10^5 . The existence of such a dynamo suggests that accretion disks can generate self-sustained magnetic fields without relying on large-scale fields from the central object. These results were published in Physical Review Letters with the Editor’s Suggestion Tag and were featured in the main website of the journal.
Publications
- Transition to magnetorotational turbulence in Taylor–Couette flow with imposed azimuthal magnetic field. New Journal of Physics, 17, 093018:1–14 (2015)
A. Guseva, A.P. Willis, R. Hollerbach, M. Avila
(See online at https://doi.org/10.1088/1367-2630/17/9/093018) - Azimuthal magnetorotational instability at low and high magnetic Prandtl numbers. Magnetohydrodynamics, 53, 1:25–34 (2017)
A. Guseva, A.P. Willis, R. Hollerbach, M. Avila
- Dynamo action in a quasi-Keplerian Taylor–Couette flow. Physical Review Letters, 119, 164501 (2017)
A. Guseva, A.P. Willis, R. Hollerbach, M. Avila
(See online at https://doi.org/10.1103/PhysRevLett.119.164501) - Transport properties of the azimuthal magnetorotational instability. The Astrophysical Journal, 849(2), 92 (2017)
A. Guseva, A.P. Willis, R. Hollerbach, M. Avila
(See online at https://doi.org/10.3847/1538-4357/aa917d) - Nonlinear evolution of helical magnetorotational instability in a magnetized Taylor–Couette flow. New Journal of Physics, 20, 013012 (2018)
G. Mamatsashvili, F. Stefani, A. Guseva, M. Avila
(See online at https://doi.org/10.1088/1367-2630/aa9d65)
