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arXiv · 2002.02630

Fully nonlinear mode competitions in magnetised Taylor-Couette flow

R. Ayats·K. Deguchi·F. Mellibovsky·A. Meseguer
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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 (2013). Mode competition phenomena are studied in both the anti-cyclonic and cyclonic Rayleigh-stable regimes. In the anti-cyclonic sub-rotation regime, with the inner cylinder rotating faster than the outer, Hollerbach, Teeluck & Rudiger (2010) 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 (2017) recently found a non-axisymmetric purely hydrodynamic linear instability that coexists with the non-axisymmetric magneto-rotational instability discovered a little earlier by Rudiger, Schultz, Gellert & Stefani (2016). We show that nonlinear interactions of these instabilities give rise to rich pattern-formation phenomena leading to drastic angular momentum transport enhancement/reduction.

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R. Ayats, K. Deguchi, F. Mellibovsky, A. Meseguer. 2020-05-02. Fully nonlinear mode competitions in magnetised Taylor-Couette flow. https://doi.org/10.1017/jfm.2020.365

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