Magnetoconvection transient dynamics by numerical simulation

  • Sébastien Renaudière de Vaux
  • Rémi Zamansky
  • Wladimir Bergez
  • Philippe Tordjeman
  • Jean-François Haquet
Regular Article


We investigate the transient and stationary buoyant motion of the Rayleigh-Bénard instability when the fluid layer is subjected to a vertical, steady magnetic field. For Rayleigh number, Ra, in the range 103-106, and Hartmann number, Ha, between 0 and 100, we performed three-dimensional direct numerical simulations. To predict the growth rate and the wavelength of the initial regime observed with the numerical simulations, we developed the linear stability analysis beyond marginal stability for this problem. We analyzed the pattern of the flow from linear to nonlinear regime. We observe the evolution of steady state patterns depending on \(Ra/Ha^{2}\) and Ha. In addition, in the nonlinear regime, the averaged kinetic energy is found to depend on Ra and to be independent of Ha in the studied range.

Graphical abstract


Flowing matter: Nonlinear Physics 

Supplementary material

10189_2017_371_MOESM1_ESM.avi (6.6 mb)
Supplementary material
10189_2017_371_MOESM2_ESM.avi (4.1 mb)
Supplementary material
10189_2017_371_MOESM3_ESM.avi (7.3 mb)
Supplementary material
10189_2017_371_MOESM4_ESM.avi (5.1 mb)
Supplementary material


  1. 1.
    S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability (Clarendon Press, 1961)Google Scholar
  2. 2.
    R. Moreau, Prog. Crystal Growth 38, 161 (1999)CrossRefGoogle Scholar
  3. 3.
    H. Branover, Metallurgical Technologies, Energy Conversion, and Magnetohydrodynamic Flows, Vol. 148 (AIAA, 1993)Google Scholar
  4. 4.
    Ch. Journeau, P. Piluso, J.F. Haquet, S. Saretta, E. Boccaccio, J.M. Bonnet, Proc. ICAPP (2007)Google Scholar
  5. 5.
    E. Taberlet, Y. Fautrelle, J. Fluid Mech. 159, 409 (1985)ADSCrossRefGoogle Scholar
  6. 6.
    J.M. Aurnou, P.L. Olson, J. Fluid Mech. 430, 283 (2001)ADSCrossRefGoogle Scholar
  7. 7.
    U. Burr, U. Müller, Phys. Fluids 13, 3247 (2001)ADSCrossRefGoogle Scholar
  8. 8.
    N.O. Weiss, M.R.E. Proctor, Magnetoconvection (Cambridge University Press, 2014)Google Scholar
  9. 9.
    Y. Nakagawa, Nature 175, 417 (1955)ADSCrossRefGoogle Scholar
  10. 10.
    Y. Nakagawa, Proc. R. Soc. London, Ser. A 240, 108 (1957)ADSCrossRefGoogle Scholar
  11. 11.
    F.H. Busse, R.M. Clever, Phys. Fluids 25, 931 (1982)ADSCrossRefGoogle Scholar
  12. 12.
    Y. Nandukumar, P. Pal, EPL 112, 24003 (2015)ADSCrossRefGoogle Scholar
  13. 13.
    W.M. Macek, M. Strumik, Phys. Rev. Lett. 112, 074502 (2014)ADSCrossRefGoogle Scholar
  14. 14.
    A. Basak, R. Raveendran, K. Kumar, Phys. Rev. E 90, 033002 (2014)ADSCrossRefGoogle Scholar
  15. 15.
    A. Basak, K. Kumar, Eur. Phys. J. B 88, 1 (2015)CrossRefGoogle Scholar
  16. 16.
    T. Yanagisawa, Y. Yamagishi, Y. Hamano, Y. Tasaka, M. Yoshida, K. Yano, Y. Takeda, Phys. Rev. E 82, 016320 (2010)ADSCrossRefGoogle Scholar
  17. 17.
    T. Yanagisawa, Y. Hamano, T. Miyagoshi, Y. Yamagishi, Y. Tasaka, Y. Takeda, Phys. Rev. E 88, 063020 (2013)ADSCrossRefGoogle Scholar
  18. 18.
    Y. Takeda, Ultrasonic Doppler Velocity Profiler for Fluid Flow, Vol. 101 (Springer Science & Business Media, 2012)Google Scholar
  19. 19.
    R. Moreau, Magnetohydrodynamics (Springer Science & Business Media, 1990)Google Scholar
  20. 20.
    M.J. Assael, I.J. Armyra, J. Brillo, S.V. Stankus, J. Wu, W.A. Wakeham, J. Phys. Chem. Ref. Data 41, 033101 (2012)ADSCrossRefGoogle Scholar
  21. 21.
    G. Grötzbach, J. Comput. Phys. 49, 241 (1983)ADSCrossRefGoogle Scholar
  22. 22.
    J. Magnaudet, M. Rivero, J. Fabre, J. Fluid Mech. 284, 97 (1995)ADSCrossRefGoogle Scholar
  23. 23.
    S. Balay, S. Abhyankar, M.F. Adams, J. Brown, P. Brune, K. Buschelman, L. Dalcin, V. Eijkhout, W.D. Gropp, D. Kaushik, M.G. Knepley, L.C. McInnes, K. Rupp, B.F. Smith, S. Zampini, H. Zhang, PETSc users manual, Technical Report ANL-95/11 - Revision 3.6 (Argonne National Laboratory, 2015)Google Scholar
  24. 24.
    S.W. Morris, E. Bodenschatz, D.S. Cannell, G. Ahlers, Phys. Rev. Lett. 71, 2026 (1993)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • Sébastien Renaudière de Vaux
    • 1
    • 2
  • Rémi Zamansky
    • 1
  • Wladimir Bergez
    • 1
  • Philippe Tordjeman
    • 1
  • Jean-François Haquet
    • 2
  1. 1.Institut de Mécanique des Fluides de Toulouse (IMFT)Université de Toulouse, CNRS-INPT-UPSToulouseFrance
  2. 2.CEA, DENCadarache, SMTA/LPMAPaul lez DuranceFrance

Personalised recommendations