Mean flow in hexagonal convection: stability and nonlinear dynamics

Abstract

Weakly nonlinear hexagon convection patterns coupled to mean flow are investigated within the framework of coupled Ginzburg-Landau equations. The equations are in particular relevant for non-Boussinesq Rayleigh-Bénard convection at low Prandtl numbers. The mean flow is found to (1) affect only one of the two long-wave phase modes of the hexagons and (2) suppress the mixing between the two phase modes. As a consequence, for small Prandtl numbers the transverse and the longitudinal phase instability occur in sufficiently distinct parameter regimes that they can be studied separately. Through the formation of penta-hepta defects, they lead to different types of transient disordered states. The results for the dynamics of the penta-hepta defects shed light on the persistence of grain boundaries in such disordered states.

33 pages, 20 figures. For better figures:http://astro.uchicago.edu/~young/hexmeandir

References in corpus (1)

• Sideband Instabilities and Defects of Quasipatterns

Cited by in corpus (7)

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• Penta-hepta defect chaos in a model for rotating hexagonal convection
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• Whirling Hexagons and Defect Chaos in Hexagonal Non-Boussinesq Convection
• Instabilities and Spatio-temporal Chaos of Long-wave Hexagon Patterns in Rotating Marangoni Convection
• Induced defect nucleation and side-band instabilities in hexagons with rotation and mean flow
• Fluid flow and spatiotemporal chaos in chemically active emulsions