Journal of Fluid Mechanics

Papers

Travelling convectons in binary fluid convection

Isabel Mercadera1 c1, Oriol Batistea1, Arantxa Alonsoa1 and Edgar Knoblocha2

a1 Departament de Física Aplicada, Universitat Politècnica de Catalunya, 08034 Barcelona, Spain

a2 Department of Physics, University of California, Berkeley, CA 94720, USA

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.

(Received May 16 2012)

(Revised January 28 2013)

(Accepted February 04 2013)

(Online publication March 28 2013)

Key words

  • buoyancy-driven instability;
  • double diffusive convection;
  • pattern formation

Correspondence

c1 Email address for correspondence: maria.isabel.mercader@upc.edu

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