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Finite amplitude convection with changing mean temperature. Part 1. Theory

Published online by Cambridge University Press:  28 March 2006

Ruby Krishnamurti
Ruby Krishnamurti
Affiliation:
Institute of Geophysics and Planetary Physics, University of California, Los Angeles, California
Present address: Institute of Geophysical Fluid Dynamics, Florida State University, Tallahassee, Florida, 32306.
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Abstract

When a horizontal layer of fluid is heated from below and cooled from above with the mean temperature and physical parameters of the fluid constant, the two-dimensional roll is known to be the stable solution near the critical Rayleigh number. In this study, with the mean temperature changing steadily at a rate η, the Rayleigh number and the velocity and temperature fields governed by the Boussinesq equations are expanded in two parameters: η, and the amplitude ε. Hexagons are shown to be the stable solution near the critical Rayleigh number. The direction of the motion depends upon the sign of η. A finite amplitude instability is possible with an associated hysteresis in the heat flux as the critical Rayleigh number is approached from below or from above.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 33 , Issue 3 , 2 September 1968 , pp. 445 - 455
Copyright
© 1968 Cambridge University Press

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