Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-19T00:06:41.287Z Has data issue: false hasContentIssue false
  • English
  • Français

A stability criterion for steady finite amplitude convection with an external magnetic field

Published online by Cambridge University Press:  28 March 2006

Dietrich Lortz
Dietrich Lortz
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology
Get access Rights & Permissions [Opens in a new window]

Abstract

In a horizontal layer of fluid, thermal expansion or the presence of dissolved salt may cause a density gradient opposite to the direction of gravity. In such cases, when the buoyancy forces are sufficient to overcome the dissipative effects, the static state becomes unstable and convective motions arise. If the layer is infinitely large in horizontal extent, the non-linear convection problem is highly degenerate, admitting many different steady-state solutions. A general necessary criterion for stability of such non-linear steady solutions is developed here for the case in which a homogeneous vertical magnetic field acts on the fluid. The criterion is demonstrated for two rigid bounding surfaces which are perfect thermal and electrical conductors, but it is applicable to more general kinds of boundary conditions.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 23 , Issue 1 , September 1965 , pp. 113 - 128
Copyright
© 1965 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

Busse, F. 1962 Dissertation, University of Munich.
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Oxford: Clarendon Press.
Lortz, D. 1961 Dissertation, University of Munich.
Malkus, W. V. R. 1954a Proc. Roy. Soc. A, 225, 185.
Malkus, W. V. R. 1954b Proc. Roy. Soc. A, 225, 196.
Malkus, W. V. R. & Veronis, G. 1958 J. Fluid Mech. 4, 225.
Palm, E. 1960 J. Fluid Mech. 8, 183.
Pellew, A. & Southwell, R. V. 1940 Proc. Roy. Soc. A, 176, 312.
Schlüter, A., Lortz, D. & Busse, F. 1965 J. Fluid Mech. 23, 129.
Segel, L. 1962 J. Fluid Mech. 14, 97.
Segel, L. 1965 (to appear in J. Fluid Mech.).
Stern, M. E. 1960 Tellus, 12, 172.
Veronis, G. 1959 J. Fluid Mech. 5, 401.