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Dynamic bifurcations and pattern formation in melting-boundary convection

Published online by Cambridge University Press:  23 September 2011

G. M. Vasil  and
M. R. E. Proctor
G. M. Vasil*
Affiliation:
Canadian Institute for Theoretical Astrophysics, 60 St George Street, Toronto, ON M5S 3H8, Canada JILA, University of Colorado, Boulder, CO 80309-0440, USA
M. R. E. Proctor
Affiliation:
Department of Applied Mathematics & Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, UK
*
†Email address for correspondence: vasil@cita.utoronto.ca
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Abstract

We consider weakly nonlinear convection in a fluid layer with a melting top boundary. This leads us to derive a new set of non-autonomous envelope equations as a dynamic generalization to the well-known Ginzburg–Landau equation. However, this new system possesses a number of interesting properties not found in systems close to a traditional dynamic bifurcation, because it involves the interaction of two destabilizing mechanisms. We investigate the system both analytically and numerically; specifically, we find the robust ‘locking in’ of spatially complex patterns, and show this is a general feature of systems of this nature.

JFM classification

Convection: Buoyancy-driven instability Phase change: Morphological instability Phase change: Solidification/melting
Type
Papers
Information
Journal of Fluid Mechanics , Volume 686 , 10 November 2011 , pp. 77 - 108
Copyright
Copyright © Cambridge University Press 2011

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