Hostname: page-component-5c6d5d7d68-7tdvq Total loading time: 0 Render date: 2024-08-10T01:07:33.613Z Has data issue: false hasContentIssue false
  • English
  • Français

The effect of centrifugal acceleration on axisymmetric convection in a shallow rotating cylinder or annulus

Published online by Cambridge University Press:  19 April 2006

P. G. Daniels
P. G. Daniels
Affiliation:
Department of Mathematics, The City University, Northampton Square, London, EC1V 0HB
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper considers the nature of stationary axisymmetric convection in a shallow rotating annulus or cylinder heated from below. The horizontal and vertical walls of the container are assumed to be perfect conductors and insulators respectively. The critical regime is considered in which the circulations due to the centrifugal force and the vertical gravitational instability are of equal significance. Among the effects of the centrifugal acceleration on the gravitational instability are a shift in the value of the Rayleigh number at which instability sets in, a modification in the distribution and amplitude of convection cells in the container and, most significantly, a smooth transition to finite amplitude convection as the Rayleigh number is increased.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 99 , Issue 1 , 11 July 1980 , pp. 65 - 84
Copyright
© 1980 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

Barcilon, V. & Pedlosky, J. 1967 J. Fluid Mech. 29, 673.
Brown, S. N. & Stewartson, K. 1978 Proc. Roy. Soc. A 360, 455.
Brown, S. N. & Stewartson, K. 1979 Siam J. Appl. Math. 36, 573.
Chandrasekhar, S. 1962 Hydrodynamic and Hydromagnetic Stability. Oxford University Press.
Daniels, P. G. 1977 Proc. Roy. Soc. A 358, 173.
Daniels, P. G. 1978 Proc. Roy. Soc. A 363, 195.
Homsy, G. M. & Hudson, J. L. 1969 J. Fluid Mech. 35, 33.
Homsy, G. M. & Hudson, J. L. 1971 J. Fluid Mech. 48, 605.
Hudson, J. L., Abell, S. & Tang, D. 1978 J. Fluid Mech. 86, 146.
Koschmieder, E. L. 1967 Beitr. Phys. Atmos. 40, 216.
Mihaljan, J. M. 1962 Astrophys. J. 136, 1126.
Newell, A. C. & Whitehead, J. A. 1969 J. Fluid Mech. 38, 279.
Rossby, H. T. 1969 J. Fluid Mech. 36, 309.
Segel, L. A. 1969 J. Fluid Mech. 38, 203.
Veronis, G. 1959 J. Fluid Mech. 5, 401.