Supercritical regimes of liquid-metal fluid motions in electromagnetic fields: wall-bounded flows
Supercritical regimes of liquid-metal fluid motions in electromagnetic fields: wall-bounded flows
An instability analysis of two-dimensional liquid-metal flows in a straight duct with free-slip boundary condition applied on the walls y = 0 and y = 2~ is conducted. The basic flow under examination is a Kolmogorov flow and it is driven by a transverse magnetic field interacting with an electric current supplied by lines of electrodes positioned in the bottom of the duct. It is proved by a rigorous theoretical analysis that all the secondary flows transitional from the basic flow are self-oscillations and that some secondary flows only arise when the Reynolds number R passes through a critical value Rc. That is, the instabilities are analytically proved to be supercritical Hopf bifurcations. Simple numerical predictions confirm the theoretical analysis.
instabilities, two-dimensional fluid motions, self-oscillations
2735-2757
Chen, Zhi-Min
e4f81e6e-5304-4fd6-afb2-350ec8d1e90f
Price, W.G.
b7888f47-e3fc-46f4-9fb9-7839052ff17c
2002
Chen, Zhi-Min
e4f81e6e-5304-4fd6-afb2-350ec8d1e90f
Price, W.G.
b7888f47-e3fc-46f4-9fb9-7839052ff17c
Chen, Zhi-Min and Price, W.G.
(2002)
Supercritical regimes of liquid-metal fluid motions in electromagnetic fields: wall-bounded flows.
Proceedings of the Royal Society A, 458 (2027), .
(doi:10.1098/rspa.2002.1002).
Abstract
An instability analysis of two-dimensional liquid-metal flows in a straight duct with free-slip boundary condition applied on the walls y = 0 and y = 2~ is conducted. The basic flow under examination is a Kolmogorov flow and it is driven by a transverse magnetic field interacting with an electric current supplied by lines of electrodes positioned in the bottom of the duct. It is proved by a rigorous theoretical analysis that all the secondary flows transitional from the basic flow are self-oscillations and that some secondary flows only arise when the Reynolds number R passes through a critical value Rc. That is, the instabilities are analytically proved to be supercritical Hopf bifurcations. Simple numerical predictions confirm the theoretical analysis.
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Published date: 2002
Keywords:
instabilities, two-dimensional fluid motions, self-oscillations
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Local EPrints ID: 23651
URI: http://eprints.soton.ac.uk/id/eprint/23651
ISSN: 1364-5021
PURE UUID: 06f28be9-11a1-4bac-9fc6-032f590c4bee
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Date deposited: 28 Mar 2006
Last modified: 15 Mar 2024 06:49
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Author:
Zhi-Min Chen
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