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Instabilities of convection rolls in a high Prandtl number fluid

Published online by Cambridge University Press:  29 March 2006

F. H. Busse  and
J. A. Whitehead
F. H. Busse
Affiliation:
Department of Planetary and Space Science, University of California, Los Angeles
J. A. Whitehead
Affiliation:
Institute of Geophysics and Planetary Physics, University of California, Los Angeles
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Abstract

An experiment on the stability of convection rolls with varying wave-number is described in extension of the earlier work by Chen & Whitehead (1968). The results agree with the theoretical predictions by Busse (1967a) and show two distinct types of instability in the form of non-oscillatory disturbances. The ‘zigzag instability’ corresponds to a bending of the original rolls; in the ‘cross-roll instability’ rolls emerge at right angles to the original rolls. At Rayleigh numbers above 23,000 rolls are unstable for all wave-numbers and are replaced by a three-dimensional form of stationary convection for which the name ‘bimodal convection’ is proposed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 47 , Issue 2 , 31 May 1971 , pp. 305 - 320
Copyright
© 1971 Cambridge University Press

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References

Busse, F. H. 1967a On the stability of two-dimensional convection in a layer heated from below J. Math. and Phys. 46, 140–149.Google Scholar
Busse, F. H. 1967b The stability of finite amplitude cellular convection and its relation to an extremum principle J. Fluid Mech. 30, 625–649.Google Scholar
Busse, F. H. 1969 On Howard's upper bound for heat transport by turbulent convection J. Fluid Mech. 37, 457–477.Google Scholar
Busse, F. H. 1970 Stability regions of cellular fluid flow. Proceedings of the IUTAM-Symposium, Herrenalb 1969. In press.Google Scholar
Chen, M. M. & Whitehead, J. A. 1968 Evolution of two-dimensional periodic Rayleigh convection cells of arbitrary wave-numbers J. Fluid Mech. 31, 1–15.Google Scholar
Krishnamurti, R. 1970a On the transition to turbulent convection. Part 1. Transition from two to three-dimensional flow J. Fluid Mech. 42, 295–307.Google Scholar
Krishnamurti, R. 1970b On the transition to turbulent convection. Part 2. Transition to time-dependent flow J. Fluid Mech. 42, 309–320.Google Scholar
Malkus, W. V. R. 1954 Discrete transitions in turbulent convection. Proc. Roy. Soc A 225, 185–195.Google Scholar
Rossby, H. T. 1969 A study of Bénard convection with and without rotation J. Fluid Mech. 36, 309–335.Google Scholar
SchlÜter, A., Lortz, D. & Busse, F. 1965 On the stability of steady finite amplitude convection J. Fluid Mech. 28, 223–239.Google Scholar
Schmidt, R. T. & Saunders, O. A. 1938 On the motion of a fluid heated from below. Proc. Roy. Soc A 165, 216–228.Google Scholar
Willis, G. E. & Deardorff, J. W. 1967 Confirmation and renumbering of the discrete heat flux transition of Malkus Phys. Fluids, 10, 1861–1866.Google Scholar