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Heteroclinic bifurcations in a simple model of double-diffusive convection

Published online by Cambridge University Press:  26 April 2006

E. Knobloch ,
M. R. E. Proctor  and
N. O. Weiss
E. Knobloch
Affiliation:
Department of Physics, University of California, Berkeley, CA 94720, USA
M. R. E. Proctor
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK
N. O. Weiss
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK
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Abstract

Two-dimensional thermosolutal convection is perhaps the simplest example of an idealized fluid dynamical system that displays a rich variety of dynamical behaviour which is amenable to investigation by a combination of analytical and numerical techniques. The transition to chaos found in numerical experiments can be related to behaviour near a multiple bifurcation of codimension three. The resulting third-order normal form equations provide a rational approximation to the governing partial differential equations and thereby confirm that temporal chaos is present in thermosolutal convection. The complex dynamics is associated with a heteroclinic orbit in phase space linking a pair of saddle-foci with eigenvalues satisfying Shil'nikov's criterion. The same bifurcation structure occurs in a truncated fifth-order model and numerical experiments confirm that similar behaviour extends to a significant region of parameter space.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 239 , June 1992 , pp. 273 - 292
Copyright
© 1992 Cambridge University Press

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