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Fully nonlinear mode competition in magnetised Taylor–Couette flow

Published online by Cambridge University Press:  11 June 2020

R. Ayats Open the ORCID record for R. Ayats [Opens in a new window] ,
K. Deguchi Open the ORCID record for K. Deguchi [Opens in a new window] ,
F. Mellibovsky Open the ORCID record for F. Mellibovsky [Opens in a new window]  and
A. Meseguer Open the ORCID record for A. Meseguer [Opens in a new window]
R. Ayats*
Affiliation:
Departament de Física, Universitat Politècnica de Catalunya, 08034Barcelona, Spain
K. Deguchi*
Affiliation:
School of Mathematics, Monash University, VIC 3800, Australia
F. Mellibovsky*
Affiliation:
Departament de Física, Universitat Politècnica de Catalunya, 08034Barcelona, Spain
A. Meseguer*
Affiliation:
Departament de Física, Universitat Politècnica de Catalunya, 08034Barcelona, Spain
*
†Email addresses for correspondence: [email protected], [email protected], [email protected], [email protected]
†Email addresses for correspondence: [email protected], [email protected], [email protected], [email protected]
†Email addresses for correspondence: [email protected], [email protected], [email protected], [email protected]
†Email addresses for correspondence: [email protected], [email protected], [email protected], [email protected]
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Abstract

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.

JFM classification

Nonlinear Dynamical Systems: Bifurcation
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 897 , 25 August 2020 , A14
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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