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MHD Turbulence at Low Magnetic Reynolds Number: Present Understanding and Future Needs

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Magnetohydrodynamics

Part of the book series: Fluid Mechanics And Its Applications ((FMIA,volume 80))

This paper is an attempt to summarize the most important results and established ideas on magnetohydrodynamic (MHD) turbulence in flows of liquid metals when the magnetic Reynolds number is significantly smaller than unity. It is written on the basis of the round-table discussion organised during the Coventry meeting, with additions introduced by the authors, coming from their own vision of the subject, or raised during their exchanges with other specialists. It covers the turbulent regimes observable in rather well controlled laboratory experiments as well as in metal processes where electromagnetic devices are used for different purposes (stirring, pumping, refining, etc). A number of still not-understood points are mentioned and some needs of new efforts are underlined.

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References

  1. Lielausis O (1975) Liquid metal magnetohydrodynamics. Atomic Energy Rev 13:527-581

    Google Scholar 

  2. Tsinober A (1975) Magnetohydrodynamic turbulence. Magnetohydrodynamics 11:5-17

    MathSciNet  Google Scholar 

  3. Tsinober A (1990) MHD flow drag reduction. In: Bushnell DM, Hefner JN (eds) Viscous Drag Reduction in Boundary layers. AIAA 123:327-349

    Google Scholar 

  4. Pope S (2000) Turbulent Flows. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  5. Moffatt HK (1967) On the suppression of turbulence by a uniform magnetic field. J Fluid Mech 28:571-592

    Article  Google Scholar 

  6. Alemany A, Moreau R, Sulem PL, Frisch U (1979) Influence of external magnetic field on homogeneous MHD turbulence. J de Mécanique 18:280-313

    Google Scholar 

  7. Caperan P, Alemany A (1985) Homogeneous low-magnetic-Reynolds-number MHD turbulence Study of the transition to the quasi-two-dimensional phase and characterization of its anisotropy. J de Mécanique Th et Appli 4:175-200

    Google Scholar 

  8. Schumann U (1976) Numerical simulation of the transition from threeto two-dimensional turbulence under a uniform magnetic field. J Fluid Mech 74:31-58

    Article  MATH  Google Scholar 

  9. Zikanov O, Thess A (1998) Direct numerical simulation of forced MHD turbu-lence at low magnetic Reynolds number. J Fluid Mech 358:299-333

    Article  MATH  Google Scholar 

  10. Knaepen B, Moin P (2004) Large-eddy simulation of conductive flows at low magnetic Reynolds number. Phys Fluids 16:1255-1261

    Article  MathSciNet  Google Scholar 

  11. Sommeria J, Moreau R (1982) Why, how and when MHD turbulence becomes two-dimensional. J Fluid Mech 118:507-518

    Article  MATH  Google Scholar 

  12. Davidson PA (1995) Magnetic damping of jets and vortices. J Fluid Mech 299:153-186

    Article  MATH  Google Scholar 

  13. Davidson PA (1997) The role of angular momentum in the magnetic damping of turbulence. J Fluid Mech 336:123-150

    Article  MATH  MathSciNet  Google Scholar 

  14. PothératA, Sommeria J, Moreau R (2000) An effective two-dimensional model for MHD flows with transverse magnetic field. J Fluid Mech 424:75-100

    Article  MATH  Google Scholar 

  15. Messadek K, Moreau R (2002) An experimental investigation of MHD quasi-2D turbulent shear flows. J Fluid Mech 456:137-159

    Article  MATH  Google Scholar 

  16. Moresco P, Alboussière T (2004) Experimental study of the instability of the Hartmann layer. J Fluid Mech 504:167-181

    Article  MATH  Google Scholar 

  17. Krasnov DS, Zienicke E, Zikanov O, Boeck T, Thess A (2004) Numerical study of the instability of the Hartmann layer. J. Fluid Mech 504:183-211

    Article  MATH  MathSciNet  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

    Article  MATH  MathSciNet  Google Scholar 

  19. Landau LD, Lifshits EM (1981) Electrodynamics of Continuous Media. 2nd edn. Nauka, Moscow, English translation by Pergamon in 1984

    Google Scholar 

  20. Kit LG, Tsinober A (1971) Possibility of creating and investigating two-dimensional turbulence in a strong magnetic field. Magnetohydrodynamics 7:312-318

    Google Scholar 

  21. Wooler PT (1961) Instability of flow between parallel planes with coplanar magnetic field. Phys Fluids 4:24-27

    Article  MATH  MathSciNet  Google Scholar 

  22. Kit LG, Turuntaev SV, Tsinober A (1970) Investigation with a conduction anemometer of the effect of a magnetic field on disturbances in the wake of a cylinder. Magnetohydrodynamics 5:331-335

    Google Scholar 

  23. Tsinober A (1996) Transition to quasi-two-dimensional turbulence and its trans-port properties in liquid metal turbulent MHD flows. Workshop on MHD-Turbulence: Experiments and Theory, IATF, FZK, Karlsruhe, 9-10, October 1996

    Google Scholar 

  24. Tsinober A (2001) An informal introduction to turbulence. Kluwer Academic, Dordrecht

    MATH  Google Scholar 

  25. Lee D, Choi H (2001) Magnetohydrodynamic turbulent flow in a channel at low magnetic Reynolds number. J Fluid Mech 439:367-394

    Article  MATH  Google Scholar 

  26. Shercliff JA (1953) Steady motion of conducting fluids in pipes under transverse magnetic fields. Proc Camb Phil Soc 49:136-144

    Article  MATH  MathSciNet  Google Scholar 

  27. Knaepen B, Dubief Y, Moreau R (2004) Hartmann effect on MHD turbulence in the limit Rm«1. In: Proceedings of the Summer Program. Stanford Center for Turbulence Research, pp 99-107

    Google Scholar 

  28. Davidson P (1999) Magnetohydrodynamics in Materials Processing. Annn Rev Fluid Mech 31:273-300

    Article  Google Scholar 

  29. Shercliff JA (1962) The theory of electromagnetic flow-measurement. Cambridge University Press, Cambridge

    Google Scholar 

  30. Kulikovski AG (1968) Slow steady flows of a conducting fluid at high Hartmann numbers. Izv Akad Nauk SSSR Mekh Zhidk i Gaza 3:3-10

    Google Scholar 

  31. Kulikovski AG (1973) Flows of a conducting incompressible liquid in an arbi-trary region with a strong magnetic field. Izv Akad Nauk SSSR Mekh Zhidk i Gaza 8:144-150

    Google Scholar 

  32. Hunt JCR, Shercliff JA (1971) Magnetohydrodynamics at high Hartmann numbers. Annn Rev Fluid Mech 3:37-62

    Article  Google Scholar 

  33. Holroyd RJ, Walker JS (1978) A theoretical study of the effect of wall conduc-tivity, non-uniform magnetic fields and variable-area ducts on liquid-metal flows at high Hartmann numbers. J Fluid Mech 84:471-495

    Article  Google Scholar 

  34. Hua TQ, Walker JS (1989) Three-dimensional MHD flow in a channel with inhomogeneous electrical conductivity. Int J Engng Sci 27:1079-1091

    Article  MATH  Google Scholar 

  35. Alboussière T (2004) A geostrophic-like model for high Hartmann number flows. J Fluid Mech 521:125-154

    Article  MATH  MathSciNet  Google Scholar 

  36. Gelfgat YM, Lielausis OA, Scherbinin EV (1976) Liquid metals under the influence of electromagnetic fields. Zinatne, Riga (in Russian)

    Google Scholar 

  37. Andreev O, Kolesnikov Y, Thess A (2007) Experimental study of liquid metal channel flow under the influence of a nonuniform magnetic field. Phys Fluids 19:039902

    Article  Google Scholar 

  38. Garnier M (ed) (1997) Proceedings of the Second International Congress on Electromagnetic Processing of Materials, Paris, 27-29 May 1997

    Google Scholar 

  39. Asai S (ed) (2000) Proceedings of the Third International Congress on Electro-magnetic Processing of Materials, Nagoya, 3-6 April 2000

    Google Scholar 

  40. Fautrelle Y, Sneyd AD (2005) Surface waves created by low frequency magnetic fields. Eur J Mech B/Fluids 24:91-112

    Article  MATH  MathSciNet  Google Scholar 

  41. Kocourek V, Karcher C, Conrath M, Schulze D (2006) Stability of liquid metal drops affected by a high frequency magnetic field. Phys Rev E 74:026303

    Article  Google Scholar 

  42. Shercliff JA (1976) Technological Alfven waves. Proc IEEE 123:1035-1042

    Google Scholar 

  43. Tsinober A (1974) Liquid metal flow in a strong magnetic field. In: All-Union Conference on Engineering problems of Controlled Thermonuclear Fusion, Leningrad, pp 247-249

    Google Scholar 

  44. Tsinober A (1987) An outline of some basic problems related to the MEKKA Programme in Karlsruhe. Internal Report 8

    Google Scholar 

  45. Roberts PH (1967) An introduction to Magnetohydrodynamics. Longmans, London

    Google Scholar 

  46. Iwai K, Kameyama T, Moreau R (2003) Alfven waves excited in a liquid metal. In: Proceedings of the 4th International Conference on Electromagnetic Processing of Materials. Lyon, 14-17 October 2003: 75-86

    Google Scholar 

  47. Vatazhin A, Lyubimov G, Regirer S (1970) MHD-flows in channels. Nauka, Moscow, 672 pp, see 209-211 (in Russian)

    Google Scholar 

  48. Antimirov M, Tabachnik E (1976) MHD convection in a vertical channel. Magnetohydrodynamics 12:147-154

    Google Scholar 

  49. Kolesnikov YB, Tsinober A (1974) An experimental study of two-dimensional turbulence behind a grid. Fluid Dynamics 9:621-624

    Article  Google Scholar 

  50. Warhaft Z (2000) Passive scalars in turbulent flows. Annn Rev Fluid Mech 32:203-240

    Article  MathSciNet  Google Scholar 

  51. Siggia ED (1994) High Rayleigh number convection. Annn Rev Fluid Mech 26:137-168

    Article  MathSciNet  Google Scholar 

  52. Grossmann S, Lohse D (2000) Scaling in thermal convection: a unifying theory. J Fluid Mech 407:27-56

    Article  MATH  MathSciNet  Google Scholar 

  53. Aurnou JM, Olsen PL (2001) Experiments on Rayleigh-Bénard convection, magnetoconvection and rotating magnetoconvection in liquid Gallium. J Fluid Mech 430:283-307

    Article  MATH  Google Scholar 

  54. Burr U, Müller U (2002) Rayleigh-Bénard convection in liquid metal layers under the influence of a horizontal magnetic field. J Fluid Mech 453:345-369

    Article  MATH  Google Scholar 

  55. Burr U, Barleon L, Jochmann P, Tsinober A (2003) Magnetohydrodynamic con-vection in a vertical slot with horizontal magnetic field. J Fluid Mech 475:21-40

    Article  MATH  MathSciNet  Google Scholar 

  56. Hanjalic K, Kenjeres S (2000) Reorganisation of turbulence structure in mag-netic Rayleigh-Bénard convection: a T-RANS study. J Turbulence 1:008

    Article  MathSciNet  Google Scholar 

  57. Cioni S, Chaumat S, Sommeria J (2000) Effect of a vertical magnetic field on turbulent Rayleigh-Bénard convection. Phys Rev E 62:R4520-4523

    Article  Google Scholar 

  58. Alboussière T, Garandet JP, Moreau R (1993) Buoyancy driven convection with a uniform magnetic field. Part 1. Asymptotic analysis. J Fluid Mech 253:545-563

    Article  MATH  Google Scholar 

  59. Davoust L, Cowley MD, Moreau R, Bolcato R (1999) Bouyancy driven convec-tion with a uniform magnetic field. Part 2. Experimental investigation. J Fluid Mech 400:59-90

    Article  MATH  Google Scholar 

  60. Tagawa T, Authié G, Moreau R (2002) Buoyant flow in long vertical enclosures in the presence of a magnetic field. Part 1. Fully-established flow. Eur J Mech B/Fluids 21:383-398

    Article  MATH  Google Scholar 

  61. Authié G, Tagawa T, Moreau R (2003) Buoyant flow in long vertical enclosures in the presence of a strong horizontal magnetic field. Part 2. Finite enclosures. Eur J Mech B/Fluids 22:203-220

    Article  MATH  Google Scholar 

  62. Kazantsev AP (1967) On magnetic field amplification in a conducting fluid. Soviet JETP 53:1807-1813

    Google Scholar 

  63. Gailitis A (1974) Generation of magnetic field by mirror-symmetric turbulence. Magnetohydrodynamics 10:131-134

    Google Scholar 

  64. Novikov VG, Ruzmaikin AA, Sokolov DD (1983) Fast dynamo in reflexionally invariant random velocity field. Soviet JETP 85:909-918

    Google Scholar 

  65. Haugen NE, Brandenburg A, Dobler W (2003) Is nonhelical hydromagnetic turbulence peaked at small scales. Astrophys J 597:L141-L144

    Article  Google Scholar 

  66. Schekochihin AA, Boldyrev SA, Kulsrud RM (2002) Spectra and growth rates of fluctuating magnetic fields in the kinematic dynamo theory with large magnetic Prandtl numbers. Astrophys J 567:828-852

    Article  Google Scholar 

  67. Schekochihin AA, Maron JL, Cowley SC (2002) The small scale-structure of MHD turbulence with large magnetic Reynolds numbers. Astrophys J 576:806-813

    Article  Google Scholar 

  68. Tsinober A, Galanti B (2003) Exploratory numerical experiments on the differ-ences between genuine and “passive” turbulence. Phys Fluids 15:3514-3531

    Article  MathSciNet  Google Scholar 

  69. Gailitis A, Lielausis O, Platacis E, Gerbeth G, Stefani F (2002) Laboratory experiments on hydromagnetic dynamos. Rev Mod Phys 74:973-990

    Article  Google Scholar 

  70. Maron J, Goldreich P (2001) Simulations of incompresible MHD turbulence. Astrophys J 554:1175-1196

    Article  Google Scholar 

  71. Müller W-C, Biskamp D, Grappin R (2003) Statistical anisotropy of magneto-hydrodynamic turbulence. Phys Rev E 67:066302

    Article  MathSciNet  Google Scholar 

  72. Odier P, Pinton JF, Fauve S (1998) Advection of a magnetic field by a turbulent swirling flow. Phys Rev E 58:7397-7401

    Article  Google Scholar 

  73. Bourgoin M, Marié L, Pétrélis F, Gasquet C, Guigon A, Lecciane JB, Moulin M, Burguete J, Chiffaudel A, Daviaud F, Fauve S, Odier P, Pinton JF (2002) MHD measurements in von Karman sodium experiment. Phys Fluids 14:3046-3058

    Article  Google Scholar 

  74. Branover H, Eidelman A, Golbraikh E, Moiseev S (1999) Turbulence and struc-tures: chaos, fluctuations and helical self-organization in nature and the labora-tory. Academic Press, San Diego

    Google Scholar 

  75. Sukoriansky S, Zilberman I, Branover H (1986) Experimental studies of turbu-lence in mercury flows with transverse magnetic fields. Exp Fluids 4:11-16

    Article  Google Scholar 

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Authors and Affiliations

  1. Laboratoire EPM, ENSHMG, 95, 38402, St Martin d'Hères Cedex, France

    René Moreau

  2. Department of Mechanical Engineering, Ilmenau University of Technology, 100565, 98684, Ilmenau, Germany

    Andre Thess

  3. Department of Fluid Mechanics, Tel Aviv University, 69778, Tel Aviv, Israel

    Arkady Tsinober

Authors
  1. René Moreau
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  2. Andre Thess
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  3. Arkady Tsinober
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Moreau, R., Thess, A., Tsinober, A. (2007). MHD Turbulence at Low Magnetic Reynolds Number: Present Understanding and Future Needs. In: Magnetohydrodynamics. Fluid Mechanics And Its Applications, vol 80. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-4833-3_14

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  • DOI: https://doi.org/10.1007/978-1-4020-4833-3_14

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-4832-6

  • Online ISBN: 978-1-4020-4833-3

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