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Three-dimensional knot convection in a layer heated from below

Published online by Cambridge University Press:  21 April 2006

R. M. Clever  and
F. H. Busse
R. M. Clever
Affiliation:
Institute of Geophysics and Planetary Physics, University of California at Los Angeles, CA 90024, USA
F. H. Busse
Affiliation:
Institute of Physics, University of Bayreuth, Postfach 10 1251, 8580 Bayreuth, FRG
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Abstract

Steady three-dimensional convection flows induced by the knot instability of two-dimensional convection rolls are studied numerically for various Prandtl numbers. The Galerkin method is used to obtain the three-dimensional solutions of the basic equations in the case of rigid, infinitely conducting boundaries. These solutions exhibit the typical knot-like structure superimposed onto the basic rolls. The Nusselt number and kinetic energy of motion do not differ much for two- and three-dimensional solutions and the toroidal part of the kinetic energy associated with vertical vorticity always remains a small fraction of the total in the case of the knot solution. The analysis of the steady solutions is complemented by a stability analysis with respect to disturbances that fit the same horizontal periodicity interval as the knot solution. All instabilities correspond to Hopf bifurcations. Some example of finite-amplitude oscillatory knot convection are presented.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 198 , January 1989 , pp. 345 - 363
Copyright
1989 Cambridge University Press

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