Fully nonlinear mode competition in magnetised Taylor–Couette flow

• Published in: Journal of fluid mechanics Vol. 897
• Main Authors: Ayats, R., Deguchi, K., Mellibovsky, F., Meseguer, A.
• Format: Journal Article
• Language: English
• Published: Cambridge Cambridge University Press 25.08.2020
• Subjects: Accretion disks; Angular momentum; Biological competition; Competition; Couette flow; Cylinders; Experiments; Fluid mechanics; Fluids; Hydrodynamics; Magnetic fields; Momentum; Reynolds number; Rotating cylinders; Rotation
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/jfm.2020.365

We study the nonlinear mode competition of various spiral instabilities in magnetised Taylor–Couette flow. The resulting finite-amplitude mixed-mode solution branches are tracked using the annular-parallelogram periodic domain approach developed by Deguchi & Altmeyer ( Phys. Rev. E, vol. 87, 2013, 043017). Mode competition phenomena are studied in both the anticyclonic and cyclonic Rayleigh-stable regimes. In the anticyclonic sub-rotation regime, with the inner cylinder rotating faster than the outer, Hollerbach et al. ( Phys. Rev. Lett. , vol. 104, 2010, 044502) found competing axisymmetric and non-axisymmetric magneto-rotational linearly unstable modes within the parameter range where experimental investigation is feasible. Here we confirm the existence of mode competition and compute the nonlinear mixed-mode solutions that result from it. In the cyclonic super-rotating regime, with the inner cylinder rotating slower than the outer, Deguchi ( Phys. Rev. E, vol. 95, 2017, 021102) recently found a non-axisymmetric purely hydrodynamic linear instability that coexists with the non-axisymmetric magneto-rotational instability discovered a little earlier by Rüdiger et al. ( Phys. Fluids , vol. 28, 2016, 014105). We show that nonlinear interactions of these instabilities give rise to rich pattern-formation phenomena leading to drastic angular momentum transport enhancement/reduction.