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On the stability of steady finite amplitude convection

Published online by Cambridge University Press:  28 March 2006

A. Schlüter ,
D. Lortz  and
F. Busse
A. Schlüter
Affiliation:
Institute of Theoretical Physics, Munich University and Institute for Plasma Physics, München-Garching
D. Lortz
Affiliation:
Institute of Theoretical Physics, Munich University and Institute for Plasma Physics, München-Garching
F. Busse
Affiliation:
Institute of Theoretical Physics, Munich University and Institute for Plasma Physics, München-Garching
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Abstract

The static state of a horizontal layer of fluid heated from below may become unstable. If the layer is infinitely large in horizontal extent, the Boussinesq equations admit many different steady solutions. A systematic method is presented here which yields the finite-amplitude steady solutions by means of successive approximations. It turns out that not every solution of the linear problem is an approximation to the non-linear problem, yet there are still an infinite number of finite amplitude solutions. A similar procedure has been applied to the stability problem for these steady finite amplitude solutions with the result that three-dimensional solutions are unstable but there is a class of two-dimensional flows which are stable. The problem has been treated for both rigid and free boundaries.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 23 , Issue 1 , September 1965 , pp. 129 - 144
Copyright
© 1965 Cambridge University Press

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References

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