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Large-scale flow in turbulent convection: a mathematical model

Published online by Cambridge University Press:  21 April 2006

L. N. Howard  and
R. Krishnamurti
L. N. Howard
Affiliation:
Department of Mathematics, Florida State University, Tallahassee, Florida 32306, USA
R. Krishnamurti
Affiliation:
Department of Oceanography, Florida State University, Tallahasse, Florida 32306, USA
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Abstract

A mathematical model of convection, obtained by truncation from the two-dimensional Boussinesq equations, is shown to exhibit a bifurcation from symmetrical cells to tilted non-symmetrical ones. A subsequent bifurcation leads to time-dependent flow with similarly tilted transient plumes and a large-scale Lagrangian mean flow. This change of symmetry is similar to that occurring with the advent of a large-scale flow and transient tilted plumes seen in laboratory experiments on turbulent convection at high Rayleigh number. Though not intended as a description of turbulent convection, the model does bring out in a theoretically tractable context the possibility of the spontaneous change of symmetry suggested by the experiments.

Further bifurcations of the model lead to stable chaotic phenomena as well. These are numerically found to occur in association with heteroclinic orbits. Some mathematical results clarifying this association are also presented.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 170 , September 1986 , pp. 385 - 410
Copyright
© 1986 Cambridge University Press

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