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Three-dimensional instability of axisymmetric buoyant convection in cylinders heated from below

Published online by Cambridge University Press:  26 April 2006

M. Wanschura ,
H. C. Kuhlmann  and
H. J. Rath
M. Wanschura
Affiliation:
Center of Applied Space Technology and Microgravity, ZARM - University of Bremen, Am Fallturm, 28359 Bremen, Germany
H. C. Kuhlmann
Affiliation:
Center of Applied Space Technology and Microgravity, ZARM - University of Bremen, Am Fallturm, 28359 Bremen, Germany
H. J. Rath
Affiliation:
Center of Applied Space Technology and Microgravity, ZARM - University of Bremen, Am Fallturm, 28359 Bremen, Germany
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Abstract

The stability of steady axisymmetric convection in cylinders heated from below and insulated laterally is investigated numerically using a mixed finite-difference/Chebyshev collocation method to solve the base flow and the linear stability equations. Linear stability boundaries are given for radius to height ratios γ from 0.9 to 1.56 and for Prandtl numbers Pr = 0.02 and Pr = 1. Depending on γ and Pr, the azimuthal wavenumber of the critical mode may be m = 1, 2, 3, or 4. The dependence of the critical Rayleigh number on the aspect ratio and the instability mechanisms are explained by analysing the energy transfer to the critical modes for selected cases. In addition to these results the onset of buoyant convection in liquid bridges with stress-free conditions on the cylindrical surface is considered. For insulating thermal boundary conditions, the onset of convection is never axisymmetric and the critical azimuthal wavenumber increases monotonically with γ. The critical Rayleigh number is less then 1708 for most aspect ratios.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 326 , 10 November 1996 , pp. 399 - 415
Copyright
© 1996 Cambridge University Press

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