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Nonlinear periodic convection in double-diffusive systems

Published online by Cambridge University Press:  20 April 2006

E. Knobloch  and
M. R. E. Proctor
E. Knobloch
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW Also Institute of Astronomy, University of Cambridge. (Present address: Physics Department, University of California, Berkeley.)
M. R. E. Proctor
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW
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Abstract

We study two examples of two-dimensional nonlinear double-diffusive convection (thermohaline convection, and convection in an imposed vertical magnetic field) in the limit where the onset of marginal overstability just precedes the exchange of stabilities. In this limit nonlinear solutions can be found analytically. The branch of oscillatory solutions always terminates on the steady solution branch. If the steady solution branch is subcritical this occurs when the period of the oscillation becomes infinite, while if it is supercritical, it occurs via a Hopf bifurcation. A detailed discussion of the stability of the oscillations is given. The results are in broad agreement with the largeramplitude results obtained previously by numerical techniques.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 108 , July 1981 , pp. 291 - 316
Copyright
© 1981 Cambridge University Press

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