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Recirculating flows

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Magnetohydrodynamics

Part of the book series: Fluid Mechanics and Its Applications ((FMIA,volume 3))

Abstract

Recirculating flows (with closed streamlines) are observed in many situations. In classical hydrodynamics, they are often due to a separation of a boundary layer, for example at sharp edge of a wall (flows in cavities or below a step). Here we consider recirculating flows generated by rotational electromagnetic forces. This situation is analogous to natural convection. To a first approximation, the distribution of external forces can be simplified to the gradient of a potential, and the fluid remains at rest (see chapter 3, § II). However, as soon as we wish to refine this distribution, the differences in gravity forces between various points can make the curl non-zero. Then the resultant of the applied forces in a given fluid domain no longer passes through its centre of gravity. A torque is therefore present which generates vorticity in the fluid.

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Bibliography

  • Alemany A. and Moreau R., 1977, J. de Méca. Th. et Appl., vol. 16, n° 4, p. 625 Batchelor G. K., 1956, J. Fluid Mech., vol. 1, p. 177

    Google Scholar 

  • Benjamin T. B. and Ursell F., 1964, Proc. Roy, Soc. London, A 225, p. 505

    Article  MathSciNet  Google Scholar 

  • Bojarevics V., 1981, Magnitnaya Gidrodinamaka, n°1, p. 21, and n°2, p. 41

    Google Scholar 

  • Bojarevics V., Milere R. P. and Chudnovsky A. Yu., 1985, Magninaya Gidrodinamika n°1, p. 67

    Google Scholar 

  • Bojarevics V., Freibergs Ya., Shilova E. I. and Shcherbinin E. V., 1989, Electrically Induced Vortical Flows, Kluwer Acad. Pub.

    Google Scholar 

  • Bojarevics V. and Shilova E. I., 1977, Magnitnaya Gidrodinamika, n° 3, p. 89

    Google Scholar 

  • Burgers J. M., 1948, Adv. Appl. Mech., vol. 1, p. 197

    Google Scholar 

  • Choudary and Szekely J., 1982, Probl. Spets. Elektrometall., vol. 17, p. 9

    Google Scholar 

  • Craik A. D. D., 1985, Wave Interactions and Fluid Flows, Camb. Univ. Press

    Google Scholar 

  • Dahlberg E., 1972, Report AE-447, Aktiebolaget Atomernergi, Studsvik, Sweden

    Google Scholar 

  • Davidson P. A. and Hunt J. C. R., 1987, J. Fluid Mech., vol. 185, p. 67

    Article  ADS  MATH  Google Scholar 

  • Davidson P. A., 1989, J. Fluid Mech. vol. 209, p. 35

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Faraday M., 1831, Phil. Trans., p. 319

    Google Scholar 

  • Freiberg and Shcherbinin E. V., 1977, Magnitnaya Gidrodinamika, n°4, p. 46

    Google Scholar 

  • Galpin J. M. and Fautrelle Y., 1990, to appear in J. Fluid Mech.

    Google Scholar 

  • Hunt J. C. R. and Maxey M. R., 1980, Proc. 2nd. Beer-Sheva Seminar on MHD Flows and Turbulence,H. H. Branover and A. Yakhot, Israël Univ. Press, p. 249

    Google Scholar 

  • Koanda S. and Fautrelle Y., 1982, Proc. of the IUTAM Symp. on Metall. Appl. of MHD, Cambridge, The Metals Soc., London, p. 120

    Google Scholar 

  • Landau L. D., 1944, Doklad. Akad. Nauk SSSR, vol. 43, p. 299

    Google Scholar 

  • Launder B. E. and Spalding D. B., 1974, Appl. Mech. and Eng., vol. 3, p. 269

    Article  MATH  Google Scholar 

  • Lesieur M., 1988, Turbulence in Fluids, Kluwer Acad. Pub.

    Google Scholar 

  • Lundquist S., 1969, Ark. f. Fys., vol. 40, p. 89

    Google Scholar 

  • Mestel J., 1989, Liquid Metal MHD,J. Lielpeteris and R. Moreau, Kluwer Acad. Pub. Moffatt H. K., 1965, J. Fluid Mech., vol. 22, p. 521

    Google Scholar 

  • Moore D. and Hunt J. C. R., 1982, Proc. of the IUTAM Symp. on Metall. Appl. of MHD, Cambridge, The Metals Soc. London, p. 93

    Google Scholar 

  • Paton B. E., Medovar B. I. and Emelyanenko Yu. G., 1981, Proc. of the 8th. Joint Symp. Ph, Chem. of Metall. Processes, Tokyo, p. 241

    Google Scholar 

  • Robinson T. and Larsson K., 1973, J. Fluid Mech., vol. 60, p. 641

    Article  ADS  Google Scholar 

  • Shcherbinin E. V., 1989, Liquid Metal MHD, ed. J. Lielpetris and R. Moreau, p. 169

    Google Scholar 

  • Shercliff J. A., 1970, J. Fluid Mech., vol. 40, p. 241

    Article  ADS  MATH  Google Scholar 

  • Shilova E. I., 1975, Magnitnaya Gidrodinamika, n°2, p. 142

    Google Scholar 

  • Sozou C., 1971, J. Fluid Mech., vol. 46, p. 25

    Article  ADS  MATH  Google Scholar 

  • Sozou C. and Pickering W. M., 1975, J. Fluid Mech., vol. 70, p. 509

    Article  ADS  MATH  Google Scholar 

  • Sozou C. and Pickering W. M., 1976, J. Fluid Mech., vol. 73, p. 641

    Article  ADS  MATH  Google Scholar 

  • Squire H. B., 1951, Quart. J. Mech. Appl. Math., vol. 4, p. 321

    MathSciNet  MATH  Google Scholar 

  • Smyslov Yu. N. and Shcherbinin E. V., 1976, Problems of Mathematical Physics, Leningrad, Nauka, p. 271 (in Russian)

    Google Scholar 

  • Szekely J. and Chang C., 1977, Iron and Steelmaking, vol. 3, p. 190 and 196

    Google Scholar 

  • Szekely J. and Naganishi K., 1975, Metall. Trans., vol. 6B, p. 245

    Google Scholar 

  • Taberlet E., 1984, Le Brassage Turbulent dans les Fours d Induction, Thèse, Grenoble

    Google Scholar 

  • Taberlet E. and Fautrelle Y., 1985, J. Fluid Mech., vol. 189, p. 409

    Article  ADS  Google Scholar 

  • Tacke K. H. and Sch vertveger K., 1979, Stahl und Eisen, vol. 89, p. 7

    Google Scholar 

  • Tarapore E. D. and Evans J. W., 1976, Metall. Trans., vol. 7B, p. 343

    Article  Google Scholar 

  • Townsend A. A., 1956, The Structure of Turbulent Shear Flow, Camb. Univ. Press

    Google Scholar 

  • Trakas C., Tabeling P. and Chabrerie J. P., 1984, J. Méca. Th. et Appl., vol. 3, p. 345

    Google Scholar 

  • Vlasyuk V. Kh., 1987, Magnitnaya Gidrodinamika, n°4, p. 101

    Google Scholar 

  • Vonnegut B., 1960, J. Geophys. Research, vol. 65, p. 203

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Laboratoire MADYLAM, Ecole Nationale Supérieure d’Hydraulique et de Mécanique, Institut National Polytechnique de Grenoble, Boîte Postale 95, 38402, Saint Martin d’Hères Cedex, France

    René Moreau

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  1. René Moreau
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© 1990 Springer Science+Business Media Dordrecht

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Moreau, R. (1990). Recirculating flows. In: Magnetohydrodynamics. Fluid Mechanics and Its Applications, vol 3. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-7883-7_6

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  • DOI: https://doi.org/10.1007/978-94-015-7883-7_6

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-4077-0

  • Online ISBN: 978-94-015-7883-7

  • eBook Packages: Springer Book Archive

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