Hostname: page-component-76fb5796d-skm99 Total loading time: 0 Render date: 2024-04-26T10:36:31.089Z Has data issue: false hasContentIssue false
  • English
  • Français

Compressible magnetoconvection in oblique fields: linearized theory and simple nonlinear models

Published online by Cambridge University Press:  26 April 2006

P. C. Matthews ,
N. E. Hurlburt ,
M. R. E. Proctor  and
D. P. Brownjohn
P. C. Matthews
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK
N. E. Hurlburt
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK Present address: Lockheed Palo Alto Research Laboratory.
M. R. E. Proctor
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK
D. P. Brownjohn
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK
Get access Rights & Permissions [Opens in a new window]

Abstract

The linear stability of a layer of compressible fluid, permeated by an oblique magnetic field, is discussed. It is shown that regardless of the system parameters, all bifurcations generically lead to travelling waves. Wave speeds and direction of the wave propagation are investigated. Symmetry arguments are used to show that when the field is almost vertical, waves with a wave vector aligned with the tilt are preferred over those with a wave vector perpendicular to the tilt. The nonlinear development of the travelling waves is explored using simple model equations.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 240 , July 1992 , pp. 559 - 569
Copyright
© 1992 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Arter, W. 1983 Nonlinear convection in an imposed horizontal magnetic field. Geophys. Astrophys. Fluid Dyn. 25, 259–292.Google Scholar
Brownjohn, D. P., Hurlburt, N. E., Proctor, M. R. E. & Weiss, N. O. 1992 Nonlinear compressible magnetoconvection. Part 3. Travelling waves and standing waves in a horizontal field (in preparation).
Cattaneo, F. 1984 Oscillatory convection in sunspots. In The Hydromagnetics of the Sun (ed. T. D. Guyenne), pp. 47–50 ESA SP 220.
Dangelmayr, G. & Knobloch, E. 1987 The Takens-Bogdanov bifurcation with. O(2) symmetry. Phil. Trans. R. Soc. Lond. A 322, 243–279.Google Scholar
Eltayeb, I. A. 1975 Overstable hydromagnetic convection in a rotating fluid layer. J. Fluid Mech. 71, 161–179.Google Scholar
Hurlburt, N. E., Matthews, P. C. & Proctor, M. R. E. 1992 Nonlinear compressible convection in an oblique magnetic field (in preparation).
Hurlbert, N. E., Proctor, M. R. E., Weiss, N. O. & Brownjohn, D. P. 1989 Nonlinear compressible magnetoconvection Part 1. Travelling waves and oscillations. J. Fluid Mech. 207, 587–628.Google Scholar
Hurlburt, N. E. & Toomre, J. 1988 Magnetic fields interacting with nonlinear compressible convection. Astrophys. J. 327, 920–932.Google Scholar
Knobloch, E. 1986 On convection in a horizontal magnetic field with periodic boundary conditions. Geophys. Astrophys. Fluid Dyn. 36, 161–177.Google Scholar
Nordlund, Ar. & Stein, R. F. 1989 Simulating magnetoconvection. In Solar and Stellar Granulation (ed. R. J. Rutten & G. Severino), pp. 453–470. Kluwer
Proctor, M. R. E. & Weiss, N. O. 1982 Magnetoconvection. Rep. Prog. Phys. 45, 1317–1379.Google Scholar
Weiss, N. O., Brownjohn, D. P., Hurlburt, N. E. & Proctor, M. R. E. 1990 Oscillatory convection in sunspot umbrae. Mon. Not. R. Astr. Soc. 245, 434–452.Google Scholar