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Mean flow in hexagonal convection: stability and nonlinear dynamics

Yuan-nan Young·Hermann Riecke
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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.

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Yuan-nan Young, Hermann Riecke. 2001-07-23. Mean flow in hexagonal convection: stability and nonlinear dynamics. https://doi.org/10.1016/s0167-2789(01)00389-x

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