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Travelling convectons in binary fluid convection

Published online by Cambridge University Press:  28 March 2013

Isabel Mercader ,
Oriol Batiste ,
Arantxa Alonso  and
Edgar Knobloch
Isabel Mercader*
Affiliation:
Departament de Física Aplicada, Universitat Politècnica de Catalunya, 08034 Barcelona, Spain
Oriol Batiste
Affiliation:
Departament de Física Aplicada, Universitat Politècnica de Catalunya, 08034 Barcelona, Spain
Arantxa Alonso
Affiliation:
Departament de Física Aplicada, Universitat Politècnica de Catalunya, 08034 Barcelona, Spain
Edgar Knobloch
Affiliation:
Department of Physics, University of California, Berkeley, CA 94720, USA
*
†Email address for correspondence: [email protected]
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Abstract

Binary fluid mixtures with a negative separation ratio heated from below exhibit steady spatially localized states called convectons for supercritical Rayleigh numbers. With no-slip, fixed-temperature, no-mass-flux boundary conditions at the top and bottom stationary odd- and even-parity convectons fall on a pair of intertwined branches connected by branches of travelling asymmetric states. In appropriate parameter regimes the stationary convectons may be stable. When the boundary condition on the top is changed to Newton’s law of cooling the odd-parity convectons start to drift and the branch of odd-parity convectons breaks up and reconnects with the branches of asymmetric states. We explore the dependence of these changes and of the resulting drift speed on the associated Biot number using numerical continuation, and compare and contrast the results with a related study of the Swift–Hohenberg equation by Houghton & Knobloch (Phys. Rev. E, vol. 84, 2011, art. 016204). We use the results to identify stable drifting convectons and employ direct numerical simulations to study collisions between them. The collisions are highly inelastic, and result in convectons whose length exceeds the sum of the lengths of the colliding convectons.

JFM classification

Convection: Buoyancy-driven instability Convection: Double diffusive convection Nonlinear Dynamical Systems: Pattern formation
Type
Papers
Information
Journal of Fluid Mechanics , Volume 722 , 10 May 2013 , pp. 240 - 266
Copyright
©2013 Cambridge University Press

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