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A double-helix laminar dynamo

Published online by Cambridge University Press:  05 February 2007

L. ZABIELSKI  and
A. J. MESTEL
L. ZABIELSKI
Affiliation:
Mathematics Department, Warsaw University of Technology, OO-661 Warsaw, Poland
A. J. MESTEL
Affiliation:
Mathematics Department, Imperial College London, SW7 2AZ, UK
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Abstract

It has recently been shown that laminar, pressure-driven flow of a conducting fluid in a helical pipe can generate a dynamo. Geometrical constraints have hitherto required a relatively small Reynolds number, and a much larger magnetic Reynolds number, Rm. Here, a configuration with two interwoven helical pipes is considered which is shown to drive a dynamo at a Reynolds number of a few hundred and Rm > 30. Various computer animations of the dynamo are available with the online version of the paper. It is found that hydrodynamic instabilities may inhibit the dynamo, but may also be regularized by it. It is also shown that a dynamo pump is possible, with flow down one pipe generating a field which drives flow in the second. Movies are available with the online version of the paper.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 573 , February 2007 , pp. 237 - 246
Copyright
Copyright © Cambridge University Press 2007

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References

REFERENCES

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Zabielski and Mestel supplementary movie

Animation 1 (above) Flow is driven in opposite senses down two interwoven helical pipes with rectangular cross-section. The inside of the helices is on the left, with the z-axis vertical and r towards the right. This first animation shows a periodic oscillation for Rm=125, Re=69 which develops from an arbitrarily small initial magnetic field. From left to right, the top line of coloured plots show contours of the cross-pipe streamfunction, the downpipe velocity, the downpipe vorticity and u.jxB. The second line portrays corresponding components of the magnetic field. The contours of u.jxB are negative in regions where magnetic field is generated. During the time evolution, the structures which appear (in green) on the outer wall in the v-diagram resemble the initial stages of the hydrodynamic instability at a higher Re.

Download Zabielski and Mestel supplementary movie(Video)
Video 28 MB

Zabielski and Mestel supplementary movie

Animation 1 (above) Flow is driven in opposite senses down two interwoven helical pipes with rectangular cross-section. The inside of the helices is on the left, with the z-axis vertical and r towards the right. This first animation shows a periodic oscillation for Rm=125, Re=69 which develops from an arbitrarily small initial magnetic field. From left to right, the top line of coloured plots show contours of the cross-pipe streamfunction, the downpipe velocity, the downpipe vorticity and u.jxB. The second line portrays corresponding components of the magnetic field. The contours of u.jxB are negative in regions where magnetic field is generated. During the time evolution, the structures which appear (in green) on the outer wall in the v-diagram resemble the initial stages of the hydrodynamic instability at a higher Re.

Download Zabielski and Mestel supplementary movie(Audio)
Audio 12.1 MB

Zabielski and Mestel supplementary movie

Animation 2. At the lower value Re=27, a periodic oscillation for Rm=343 has much higher magnetic energy values compared to the first animation and so the Lorentz force perturbs the flow more.

Download Zabielski and Mestel supplementary movie(Video)
Video 17.6 MB

Zabielski and Mestel supplementary movie

Animation 2. At the lower value Re=27, a periodic oscillation for Rm=343 has much higher magnetic energy values compared to the first animation and so the Lorentz force perturbs the flow more.

Download Zabielski and Mestel supplementary movie(Audio)
Audio 11 MB

Zabielski and Mestel supplementary movie

Animation 3. For Re=27 and Rm=8000, the dynamo is a-periodic and extremely active. Unusually, in this portion of the time evolution both the kinetic and magnetic energies are decreasing, as the fine structures which develop are dissipated.

Download Zabielski and Mestel supplementary movie(Video)
Video 15.6 MB

Zabielski and Mestel supplementary movie

Animation 3. For Re=27 and Rm=8000, the dynamo is a-periodic and extremely active. Unusually, in this portion of the time evolution both the kinetic and magnetic energies are decreasing, as the fine structures which develop are dissipated.

Download Zabielski and Mestel supplementary movie(Audio)
Audio 9.7 MB