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Bistability between a stationary and an oscillatory dynamo in a turbulent flow of liquid sodium. (English) Zbl 1183.76009
Summary: We report the first experimental observation of a bistable dynamo regime. A turbulent flow of liquid sodium is generated between two disks in the von Kármán geometry (VKS experiment). When one disk is kept at rest, bistability is observed between a stationary and an oscillatory magnetic field. The stationary and oscillatory branches occur in the vicinity of a codimension-two bifurcation that results from the coupling between two modes of magnetic field. We present an experimental study of the two regimes and study in detail the region of bistability that we understand in terms of dynamical system theory. Despite the very turbulent nature of the flow, the bifurcations of the magnetic field are correctly described by a low-dimensional model. In addition, the different regimes are robust; i.e. turbulent fluctuations do not drive any transition between the oscillatory and stationary states in the region of bistability.

76-05 Experimental work for problems pertaining to fluid mechanics
76W05 Magnetohydrodynamics and electrohydrodynamics
76E25 Stability and instability of magnetohydrodynamic and electrohydrodynamic flows
76U05 General theory of rotating fluids
Full Text: DOI
[1] DOI: 10.1103/PhysRevLett.98.044502 · doi:10.1103/PhysRevLett.98.044502
[2] DOI: 10.1088/0953-8984/20/49/494203 · doi:10.1088/0953-8984/20/49/494203
[3] DOI: 10.1103/PhysRevLett.101.104501 · doi:10.1103/PhysRevLett.101.104501
[4] Guckenheimer, Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields (1986)
[5] Fuchs, Dynamo and Dynamics, a Mathematical Challenge pp 339– (2001) · doi:10.1007/978-94-010-0788-7_40
[6] DOI: 10.1209/0295-5075/87/39002 · doi:10.1209/0295-5075/87/39002
[7] DOI: 10.1103/PhysRevLett.56.724 · doi:10.1103/PhysRevLett.56.724
[8] DOI: 10.1063/1.3073745 · Zbl 1183.76158 · doi:10.1063/1.3073745
[9] DOI: 10.1046/j.1365-246X.1999.00886.x · doi:10.1046/j.1365-246X.1999.00886.x
[10] DOI: 10.1016/0022-0396(85)90076-2 · Zbl 0516.34042 · doi:10.1016/0022-0396(85)90076-2
[11] DOI: 10.1103/PhysRevA.35.4004 · doi:10.1103/PhysRevA.35.4004
[12] DOI: 10.1103/PhysRevLett.86.3024 · doi:10.1103/PhysRevLett.86.3024
[13] Chandrasekhar, Hydrodynamic and Hydromagnetic Stability (1961)
[14] DOI: 10.1209/0295-5075/77/59001 · doi:10.1209/0295-5075/77/59001
[15] Arnold, Geometrical Methods in the Theory of Ordinary Differential Equations (1982)
[16] DOI: 10.1063/1.1331315 · Zbl 1184.76529 · doi:10.1063/1.1331315
[17] Roberts, Rotating Fluids in Geophysics pp 421– (1978)
[18] DOI: 10.1103/PhysRevLett.98.254502 · doi:10.1103/PhysRevLett.98.254502
[19] DOI: 10.1103/PhysRevLett.93.164501 · doi:10.1103/PhysRevLett.93.164501
[20] DOI: 10.1103/PhysRevLett.101.074502 · doi:10.1103/PhysRevLett.101.074502
[21] DOI: 10.1103/PhysRevLett.99.224501 · doi:10.1103/PhysRevLett.99.224501
[22] DOI: 10.1080/03091920701523410 · doi:10.1080/03091920701523410
[23] DOI: 10.1103/PhysRevLett.102.144503 · doi:10.1103/PhysRevLett.102.144503
[24] DOI: 10.1063/1.3085724 · Zbl 1183.76360 · doi:10.1063/1.3085724
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