Role of uniform horizontal magnetic field on convective flow

  • P. PalEmail author
  • K. Kumar
Regular Article


The effect of uniform magnetic field applied along a fixed horizontal direction in Rayleigh-Bénard convection in low-Prandtl-number fluids has been studied using a low dimensional model. The model shows the onset of convection (primary instability) in the form of two dimensional stationary rolls in the absence of magnetic field, when the Rayleigh number R is raised above a critical value R c . The flow becomes three dimensional at slightly higher values of Rayleigh number via wavy instability. These wavy rolls become chaotic for slightly higher values of R in low-Prandtl-number (P r ) fluids. A uniform magnetic field along horizontal plane strongly affects all kinds of convective flows observed at higher values of R in its absence. As the magnetic field is raised above certain value, it orients the convective rolls in its own direction. Although the horizontal magnetic field does not change the threshold for the primary instability, it affects the threshold for secondary (wavy) instability. It inhibits the onset of wavy instability. The critical Rayleigh number R o (Q, P r ) at the onset of wavy instability, which depends on Chandrasekhar’s number Q and P r , increases monotonically with Q for a fixed value of P r . The dimensionless number R o (Q, P r ) / (R c Q P r ) scales with Q as Q −1. A stronger magnetic field suppresses chaos and makes the flow two dimensional with roll pattern aligned along its direction.


Statistical and Nonlinear Physics 


  1. 1.
    S. Chandrasekhar, Hydrodynamic and Magnetohydrody- namic Stability (Oxford University Press, Oxford, 1961) Google Scholar
  2. 2.
    M.R.E. Proctor, N.O. Weiss, Rep. Prog. Phys. 45, 1317 (1982) ADSCrossRefGoogle Scholar
  3. 3.
    D.T.J. Hurle, R.W. Series, Handbook of crystal growth, edited by D.T.J. Hurle (North Holland, Amsterdam, 1994) Google Scholar
  4. 4.
    A. Gailitis, O. Lielausis, E. Platacis, G. Gerbeth, F. Stephani, F. Rossendorf, Rev. Mod. Phys. 74, 973 (2002)ADSCrossRefGoogle Scholar
  5. 5.
    F.H. Busse, R.M. Clever, J. Mech. Theor. Appl. 2, 495 (1983)ADSzbMATHGoogle Scholar
  6. 6.
    F.H. Busse, R.M. Clever, Phys. Rev. A 40, 1954 (1989) ADSCrossRefGoogle Scholar
  7. 7.
    R.M. Clever, F.H. Busse, J. Fluid Mech. 201, 507 (1989) ADSzbMATHCrossRefGoogle Scholar
  8. 8.
    P. Pal, K. Kumar, Indian J. Phys. 81, 1215 (2007) Google Scholar
  9. 9.
    P. Sulem, C. Sulem, P.L. Sulem, O. Thual, Prog. Astro. Aeronaut. 100, 125 (1985) Google Scholar
  10. 10.
    M. Meneguzzi, C. Sulem, P.L. Sulem, O. Thual, J. Fluid Mech. 182, 169 (1987) ADSzbMATHCrossRefGoogle Scholar
  11. 11.
    O.M. Podvigina, Phys. Rev. E 81, 056322 (2010) MathSciNetADSCrossRefGoogle Scholar
  12. 12.
    Y. Nakagawa, Proc. R. Soc. A 240, 108 (1957) ADSCrossRefGoogle Scholar
  13. 13.
    Y. Nakagawa, Proc. R. Soc. A 249, 138 (1959) ADSCrossRefGoogle Scholar
  14. 14.
    B. Lehnert, N.C. Little, Tellus 9, 97 (1957)ADSCrossRefGoogle Scholar
  15. 15.
    S. Fauve, C. Laroche, A. Libchaber, J. Phys. Lett. 42, L455 (1981) CrossRefGoogle Scholar
  16. 16.
    S. Fauve, C. Laroche, A. Libchaber, J. Phys. Lett. 45, L101 (1984) CrossRefGoogle Scholar
  17. 17.
    S. Fauve, C. Laroche, A. Libchaber, B. Perrin, Phys. Rev. Lett. 52, 1774 (1984) ADSCrossRefGoogle Scholar
  18. 18.
    B. Hof, A. Juel, T. Mullin, J. Fluid Mech. 545, 193 (2005) MathSciNetADSzbMATHCrossRefGoogle Scholar
  19. 19.
    K.E. McKell, D.S. Broomhead, R. Jones, D.T.J. Hurle, Europhys. Lett. 12, 513518 (1990) CrossRefGoogle Scholar
  20. 20.
    F.H. Busse, J. Fluid Mech. 52, 97 (1972)ADSzbMATHCrossRefGoogle Scholar
  21. 21.
    P. Pal, K. Kumar, Phys. Rev. E 65, 047302 (2002) ADSCrossRefGoogle Scholar
  22. 22.
    O. Thual, J. Fluid Mech. 240, 229 (1992) ADSzbMATHCrossRefGoogle Scholar
  23. 23.
    K. Kumar, S. Fauve, O. Thual, J. Phys. II 6, 945 (1996)CrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Department of MathematicsNational Institute of TechnologyDurgapurIndia
  2. 2.Department of Physics and MeteorologyIndian Institute of TechnologyKharagpurIndia

Personalised recommendations