Chaotic wave dynamics in weakly magnetised spherical Couette flows

Abstract

Direct numerical simulations of a liquid metal filling the gap between two concentric spheres are presented. The flow is governed by the interplay between the rotation of the inner sphere (measured by the Reynolds number Re) and a weak externally applied axial magnetic field (measured by the Hartmann number Ha). By varying the latter a rich variety of flow features, both in terms of spatial symmetry and temporal dependence, is obtained. Flows with two or three independent frequencies describing their time evolution are found as a result of Hopf bifurcations. They are stable on a sufficiently large interval of Hartmann numbers where regions of multistability of two, three and even four types of these different flows are detected. The temporal character of the solutions is analysed by means of an accurate frequency analysis and Poincaré sections. An unstable branch of flows undergoing a period doubling cascade and frequency locking of three-frequency solutions is described as well.

arXiv comment32 pages, 12 figures and 3 tables

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Cited by in corpus (5)

• Experimental investigation of the return flow instability in magnetic spherical Couette flow
• Four-frequency solution in a magnetohydrodynamic Couette flow as a consequence of azimuthal symmetry breaking
• Long term time dependent frequency analysis of chaotic waves in the weakly magnetized spherical Couette system
• High dimensional tori and chaotic and intermittent transients in magnetohydrodynamic Couette flows
• Modulated rotating waves and triadic resonances in spherical fluid systems: The case of magnetized spherical Couette flow