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The interaction of two spatially resonant patterns in thermal convection. Part 1. Exact 1:2 resonance

Published online by Cambridge University Press:  21 April 2006

M. R. E. Proctor  and
C. A. Jones
M. R. E. Proctor
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK
C. A. Jones
Affiliation:
Department of Applied Mathematics, University of Newcastle-upon-Tyne, NE1 7RU, UK
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Abstract

The linear stability of two superimposed layers of fluid, heated from below and separated by a thin conducting plate, is investigated. It is shown that when the ratio of the depths of the layers is close to 1:2, two distinct modes of convection can occur with preferred horizontal wavenumber in the ratio 1:2. The nonlinear evolution of a disturbance consisting of both modes is considered, and it is shown that travelling waves are the preferred mode of nonlinear convection for a wide range of parameter values. Other possible types of behaviour, including modulated waves and an attracting homoclinic trajectory, are also described in detail.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 188 , March 1988 , pp. 301 - 335
Copyright
© 1988 Cambridge University Press

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