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Transition from hydrodynamic turbulence to magnetohydrodynamic turbulence in von Kármán flows

Published online by Cambridge University Press:  09 January 2012

Gautier Verhille ,
Ruslan Khalilov ,
Nicolas Plihon ,
Peter Frick  and
Jean-François Pinton
Gautier Verhille*
Affiliation:
Laboratoire de Physique, École Normale Supérieure de Lyon, CNRS UMR 5672 & Université de Lyon, 46 allée d’Italie, F-69364 Lyon CEDEX 07, France Institut de Recherche sur les Phénomènes Hors Équilibre, UMR 6594, CNRS & Aix-Marseille Université, 49 rue F. Joliot-Curie, BP 146, 13384 Marseille CEDEX 13, France
Ruslan Khalilov
Affiliation:
Institute of Continuous Media Mechanics, Korolev 1, Perm 614013, Russia
Nicolas Plihon
Affiliation:
Laboratoire de Physique, École Normale Supérieure de Lyon, CNRS UMR 5672 & Université de Lyon, 46 allée d’Italie, F-69364 Lyon CEDEX 07, France
Peter Frick
Affiliation:
Institute of Continuous Media Mechanics, Korolev 1, Perm 614013, Russia
Jean-François Pinton
Affiliation:
Laboratoire de Physique, École Normale Supérieure de Lyon, CNRS UMR 5672 & Université de Lyon, 46 allée d’Italie, F-69364 Lyon CEDEX 07, France
*
†Email address for correspondence: verhille@irphe.univ-mrs.fr
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Abstract

The influence of an externally applied magnetic field on flow turbulence is investigated in liquid-gallium von-Kármán (VK) swirling flows. Time-resolved measurements of global variables (such as the flow power consumption) and local recordings of the induced magnetic field are made. From these measurements, an effective Reynolds number is introduced as , so as to take into account the influence of the interaction parameter . This effective magnetic Reynolds number leads to unified scalings for both global variables and the locally induced magnetic field. In addition, when the flow rotation axis is perpendicular to the direction of the applied magnetic field, significant flow and induced magnetic field fluctuations are observed at low interaction parameter values, but corresponding to an Alfvèn speed of the order of the fluid velocity fluctuations . This strong increase in the flow fluctuations is attributed to chaotic changes between hydrodynamic and magnetohydrodynamic velocity profiles.

JFM classification

MHD and Electrohydrodynamics: Dynamo theory MHD and Electrohydrodynamics: High-Hartmann-number flows MHD and Electrohydrodynamics: MHD turbulence
Type
Papers
Information
Journal of Fluid Mechanics , Volume 693 , 25 February 2012 , pp. 243 - 260
Copyright
Copyright © Cambridge University Press 2012

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References

1. Alemany, A., Moreau, R., Sulem, P. L. & Frisch, U. 1979 Influence of an external magnetic field on homogeneous MHD turbulence. J. Méc. 18 (2), 277–313.Google Scholar
2. Biskamp, D. 2003 Magnetohydrodynamic Turbulence. Cambridge University Press.Google Scholar
3. Bourgoin, M., Volk, R., Frick, P., Khripchenko, S., Odier, P. & Pinton, J.-F. 2004 Induction mechanism in von Kármán swirling flows of liquid gallium. Magnetohydrodynamics 40 (1), 13–31.Google Scholar
4. Brito, D., Cardin, P., Nataf, H.-C. & Marolleau, G. 1995 Experimental study of a geostrophic vortex of gallium in a transverse magnetic field. Phys. Earth Planet. Inter. 91 (1–3), 77–98.Google Scholar
5. Cortet, P.-P., Chiffaudel, A., Daviaud, F. & Dubrulle, B. 2010 Experimental evidence of a phase transition in a closed turbulent flow. Phys. Rev. Lett. 105 (10), 214501.CrossRefGoogle Scholar
6. Dudley, N. L. & James, R. W. 1989 Time-dependent kinematic dynamos with stationary flows. Phil. Trans. R. Soc. Lond. A 425 (869), 407–429.Google Scholar
7. Eckert, S., Gerbeth, G., Witke, W. & Langenbrunner, H. 2001 MHD turbulence measurements in a sodium channel flow exposed to a transverse magnetic field. Intl J. Heat Transfer Fluid Flow 22 (3), 358–364.CrossRefGoogle Scholar
8. Frick, P., Noskov, V., Denisov, S. & Stepanov, R. 2010 Direct measurement of effective magnetic diffusivity in turbulent flow of liquid sodium. Phys. Rev. Lett. 150, 184502.Google Scholar
9. Gailitis, A., Lielausis, O., Platacis, E., Dement’ev, S., Cifersons, A., Gerbeth, G., Gundrum, T., Stefani, F., Christen, M. & Will, G. 2001 Magnetic field saturation in the Riga dynamo experiment. Phys. Rev. Lett. 86, 3024–3027.CrossRefGoogle ScholarPubMed
10. Gallet, B., Berhanu, M. & Mordant, N. 2009 Influence of an external magnetic field on forced turbulence in a swirling flow of liquid metal. Phys. Fluids 21 (8), 085107.Google Scholar
11. Kenjeres, S. & Hanjalic, K. 2009 Tackling complex turbulent flows with transient RANS. Fluid Dyn. Res. 41, 012201.Google Scholar
12. Klein, R. & Pothérat, A. 2010 Appearance of three dimensionality in wall-bounded MHD flows. Phys. Rev. Lett. 104 (3), 034502.Google Scholar
13. Marié, L. & Daviaud, F. 2004 Experimental measurement of the scale-by-scale momentum transport budget in a turbulent shear flow. Phys. Fluids 16 (2), 457–461.CrossRefGoogle Scholar
14. Moffatt, H. K. 1961 The amplification of a weak applied magnetic field by turbulence in fluids of moderate conductivity. J. Fluid Mech. 11, 625–635.Google Scholar
15. Moffatt, H. K. 1978 Magnetic Field Generation in Electrically Conducting Fluid. Cambridge University Press.Google Scholar
16. Monchaux, R., Berhanu, M., Aumaître, S., Chiffaudel, A., Daviaud, F., Dubrulle, B., Ravelet, F., Fauve, S., Mordant, N., Pétrélis, F., Bourgoin, M., Odier, P., Pinton, J.-F., Plihon, N. & Volk, R. 2009 The von Kármán sodium experiment: turbulent dynamical dynamos. Phys. Fluids 21, 035108.Google Scholar
17. Moreau, R. 1998 MHD turbulence at the laboratory scale: established ideas and new challenges. Appl. Sci. Res. 58 (1–4), 131–147.Google Scholar
18. Mück, B., Günther, C., Müller, U. & Bühler, L. 2000 Three-dimensional MHD flows in rectangular ducts with internal obstacles. J. Fluid Mech. 418, 265–295.Google Scholar
19. Müller, U., Stieglitz, R. & Horanyi, S. 2006 Experiments at a two-scale dynamo test facility. J. Fluid Mech. 552, 419–440.Google Scholar
20. Odier, P., Pinton, J.-F. & Fauve, S. 1998 Advection of a magnetic field by a turbulent swirling flow. Phys. Rev. E 58, 7397.Google Scholar
21. Odier, P., Pinton, J.-F. & Fauve, S. 2000 Magnetic induction by coherent vortex motion. Eur. Phys. J. B 16, 373–378.CrossRefGoogle Scholar
22. Parker, E. N. 1955 Hydromagnetic dynamo models. Astrophys. J. 122, 293–314.Google Scholar
23. Pétrélis, F., Bourgoin, M., Marié, L., Burguete, J., Chiffaudel, A., Daviaud, F., Fauve, S., Odier, P. & Pinton, J.-F. 2003 Nonlinear magnetic induction by helical motion in a liquid sodium turbulent flow. Phys. Rev. Lett. 90 (17), 174501.CrossRefGoogle Scholar
24. Ponomarenko, Y. B. 1973 Theory of the hydromagnetic generator. J. Appl. Mech. Tech. Phys. 14, 775–778.Google Scholar
25. Ravelet, F. 2005 Bifurcations globales hydrodynamiques et magnétohydrodynamiques dans un écoulement de von Kármán turbulent. PhD thesis, École doctorale de l’École Polytechnique. http://tel.archives-ouvertes.fr/tel-00011016/.Google Scholar
26. Ravelet, F., Chiffaudel, A. & Daviaud, F. 2008 Supercritical transition to turbulence in an inertially driven von Kármán closed flow. J. Fluid Mech. 601, 339–364.Google Scholar
27. Ravelet, F., Chiffaudel, A., Daviaud, F. & Léorat, J. 2005 Toward an experimental von Kármán dynamo: numerical studies for an optimized design. Phys. Fluids 17 (11), 117104.Google Scholar
28. Roberts, G. O. 1972 Dynamo action of fluid motions with two-dimensional periodicity. Phil. Trans. R. Soc. Lond. A 271 (1216), 411–454.Google Scholar
29. Sommeria, J. & Moreau, M. 1982 Why, how and when, MHD-turbulence becomes two-dimensional? J. Fluid Mech. 118, 507–518.Google Scholar
30. de la Torre, A. & Burguete, J. 2007 Slow dynamics in a turbulent von Kármán swirling flow. Phys. Rev. Lett. 99, 054101.Google Scholar
31. Volk, R., Odier, P. & Pinton, J.-F. 2006 Fluctuation of magnetic induction in von Kármán swirling flows. Phys. Fluids 18 (8), 085105.CrossRefGoogle Scholar
32. Zikanov, O. & Thess, A. 1998 Direct numerical simulation of forced MHD turbulence at low magnetic Reynolds number. J. Fluid Mech. 358, 299–333.Google Scholar