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Non-stationary finite amplitude convection

Published online by Cambridge University Press:  28 March 2006

F. H. Busse
F. H. Busse
Affiliation:
Institute of Geophysics and Planetary Physics, University of California, Los Angeles
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Abstract

There are stationary solutions of finite amplitude convection in a layer of fluid heated from below which show increasing heat transport with decreasing Rayleigh number in the neighbourhood of its critical value. It is shown that those solutions are unstable and that convection with periodic time dependence can occur in these cases, when the heat flux is the given parameter instead of the temperature difference between the boundaries of the layer. The time dependence has been calculated explicitly for the case of convection with temperature variation of the material properties.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 28 , Issue 2 , 8 May 1967 , pp. 223 - 239
Copyright
© 1967 Cambridge University Press

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References

Busse, F. H. 1962 Dissertation, University of Munich. English translation by S. H. Davis, Rand Report LT-66-19, Rand Corporation, Santa Monica, California.
Courant, R. & Hilbert, D. 1937 Methoden der Mathematischen Physik, 2, 214.CrossRef
Howard, L. N. 1964 Proc. XIth Int. Cong. Appl. Mech., Munich, 1964.
Levinson, N. & Smith, O. 1942 Duke Math. J. 9, 382.
Lortz, D. 1965 J. Fluid Mech. 23, 115.
Malkus, W. V. R. & Veronis, G. 1958 J. Fluid Mech. 4, 225.
Schlüter, A., Lortz, D. & Busse, F. 1965 J. Fluid Mech. 23, 129.
Segel, L. A. 1966 Non-Equilibrium Thermodynamics, Variational Techniques and Stability, edited by R. T. Donnelly, R. Herman & I. Prigogine. University of Chicago Press.
Stuart, J. T. 1958 J. Fluid Mech. 4, 1.
Veronis, G. 1959 J. Fluid. Mech. 5, 401.