Localized convection cells in the presence of a vertical magnetic field

Journal of Fluid Mechanics

Volumn 570, Issue , 2007, Pages 385-406

  Dawes, J H P ^a  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); COMPUTER SIMULATION; DIFFUSION; MAGNETIC FIELD EFFECTS;

MAGNETIC DIFFUSIVITY; MAGNETIC FIELD STRENGTH; THERMAL CONVECTION; THERMAL FORCING; VERTICAL MAGNETIC FIELD;

HEAT CONVECTION;

BIFURCATION (MATHEMATICS); COMPUTER SIMULATION; DIFFUSION; HEAT CONVECTION; MAGNETIC FIELD EFFECTS;

BIFURCATION; GEOMAGNETIC FIELD; GEOMAGNETISM; GEOPHYSICS; POWER LAW; SIMULATION; THERMAL CONVECTION;

EID: 33846027126     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S0022112006002795     Document Type: Article

References (32)

1. Batiste, O., Knobloch, E., Alonso, A. & Mercader, I. 2006 Spatially localized binary fluid convection. J. Fluid Mech. 560, 149-158.
2. Blanchflower, S. M. 1999a Magnetohydrodynamic convectons. Phys. Lett. A 261, 74-81.
3. Blanchflower, S. M. 1999b Modelling photospheric magnetoconvection. PhD thesis, University of Cambridge.
4. Blanchflower, S. M., Rucklidge, A. M. & Weiss, N. O. 1998 Modelling photospheric magneto-convection. Mon. Not. R. Astron. Soc. 301, 593-608.
5. Blanchflower, S. M. & Weiss, N. O. 2002 Three-dimensional magnetohydrodynamic convectons. Phys. Lett. A 294, 297-303.
6. Busse, F. H. 1975 Nonlinear interaction of magnetic field and convection. J. Fluid Mech. 71, 193-206.
7. Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Oxford University Press.
8. Coullet, P., Riera, C. & Tresser, C. 2000 Stable static localized structures in one dimension. Phys. Rev. Lett. 84, 3069-3072.
9. Cox, S. M. & Matthews, P. C. 2001 New instabilities in two-dimensional rotating convection and magnetoconvection. Physica D 149, 210-229.
10. Cox, S. M. & Matthews, P. C. 2003 Instability and localisation of patterns due to a conserved quantity. Physica D 175, 196-219.
11. Cox, S. M., Matthews, P. C. & Pollicott, S. L. 2004 Swift-Hohenberg model for magneto-convection. Phys. Rev. E 69, 066314.
12. Cross, M. C. & Hohenberg, P. C. 1993 Pattern formation outside of equilibrium. Rev. Mod. Phys. 65 851-1112.
13. Doedel, E., Champneys, A., Fairgrieve, T., Kuznetsov, Y., Sandstede, B. & Wang, X. 1997 AUTO97: Continuation and Bifurcation Software for Ordinary Differential Equations. Available via FTP from directory pub/ doedel/auto at ftp.cs.concordia.ca.
14. Hoyle, R. B. 2006 Pattern Formation: An Introduction To methods. Cambridge University Press.
15. Hunt, G. W., Peletier, M. A., Champneys, A. R., Woods, P. D., Wadee, M. A., Budd, C. J. & Lord, G. J. 2000 Cellular buckling in long structures. Nonlinear Dyn. 21, 3-29.
16. Hurlburt, N. E. & Toomre, J. 1988 Magnetic fields interacting with nonlinear compressible convection. A. J. 327, 920-932.
17. Knobloch, E., Weiss, N. O. & Da Costa, L. N. 1981 Oscillatory and steady convection in a magnetic field. J. Fluid Mech. 113, 153-186.
18. Komarova, N. L. & Newell, A. C. 2000 Nonlinear dynamics of sand banks and sand waves. J. Fluid Mech. 415, 285-321.
19. Julien, K., Knobloch, E. & Tobias, S. M. 1999 Strongly nonlinear magnetoconvection in three dimensions. Physica D 128, 105-129.
20. Lorenz, E. N. 1963 Deterministic nonperiodic flow. J. Atmos. Sci. 20, 130-141.
21. Matthews, P. C. 1999 Asymptotic solutions for nonlinear magnetoconvection. J. Fluid Mech. 387, 397-409.
22. Matthews, P. C. & Cox, S. M. 2000 Pattern formation with a conservation law. Nonlinearity 13, 1293-1320.
23. Proctor, M. R. E. & Weiss, N. O. 1982 Magnetoconvection. Rep. Prog. Phys. 45, 1317-1379.
24. Rotermund, H. H., Jakubith, S., von Oertzen, A. & Ertl, G. Solitons in a surface reaction. Phys. Rev. Lett. 66 3083-3086.
25. Sakaguchi, H. & Brand, H. R. 1996 Stable localized solutions of arbitrary length for the quintic Swift-Hohenberg equation. Physica D 97, 274-285
26. Strümpel, C., Purwins, H.-G. & Astrov, Y. A. 2001 Spatiotemporal filamentary patterns in a dc-driven planar gas discharge system. Phys. Rev. E 63 026409.
27. Swift, J. B. & Hohenberg, P. C. 1977 Hydrodynamic fluctuations at the convective instability. Phys. Rev. A 15, 319-328.
28. Umbanhowar, P. B., Melo, F. & Swinney, H. L. 1996 Localized excitations in a vertically vibrated granular layer. Nature 382, 793-796.
29. Weiss, N. O. 1966 The expulsion of magnetic flux by eddies Proc. R. Soc. Lond. A 293, 310-328.
30. Weiss, N. O. 1981a Convection in an imposed magnetic field. Part 1. The development of nonlinear convection. J. Fluid Mech. 108, 247-272.
31. Weiss, N. O. 1981b Convection in an imposed magnetic field. Part 2. The dynamical regime. J. Fluid Mech. 108, 273-289.
32. Weiss, N. O. 2002 Umbral and penumbral magnetoconvection. Astron. Nachr. 323, 371-376.