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Nonlinear oscillatory convection

Published online by Cambridge University Press:  21 April 2006

R. M. Clever  and
F. H. Busse
R. M. Clever
Affiliation:
Institut für Physik, Universität Bayreuth, 8580 Bayreuth, West-Germany
F. H. Busse
Affiliation:
Institut für Physik, Universität Bayreuth, 8580 Bayreuth, West-Germany
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Abstract

A numerical analysis has been performed of three-dimensional time-dependent solutions which bifurcate supercritically from two-dimensional convection-roll solutions at the onset of the oscillatory instability. The bifurcating solutions describe a periodic shifting forward and backward of the convection rolls and lead to a strong deformation of the rolls as the Rayleigh number increases. Since the bifurcating solution is stable in the form of a travelling wave, the computational expense can be reduced by assuming a moving coordinate. Travelling-wave solutions have been computed in the case of rigid boundaries as a function of the Prandtl number and of the two basic wavenumbers αx, αy of the problem. The onset of oscillations reduces the heat transport in comparison with that of two-dimensional rolls because the occupation of a new degree of freedom of motion by the oscillation reduces the energy of the heat-transporting component of convection. A limited stability analysis of finite-amplitude travelling waves has been performed and the onset of an asymmetric mode of oscillations is determined as a function of the parameters of the problem. This mode appears to be identical with a mode that was observed in the numerical simulations of Lipps (1976) and McLaughlin & Orszag (1982).

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 176 , March 1987 , pp. 403 - 417
Copyright
© 1987 Cambridge University Press

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