Mean flow in hexagonal convection: Stability and nonlinear dynamics

Yuan Nan Young*, Hermann Riecke

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

19 Scopus citations

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 are expected to 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.

Original languageEnglish (US)
Pages (from-to)166-183
Number of pages18
JournalPhysica D: Nonlinear Phenomena
Volume163
Issue number3-4
DOIs
StatePublished - Mar 15 2002

Keywords

  • Ginzburg-Landau equation
  • Grain boundary
  • Hexagon pattern
  • Mean flow
  • Nonlinear phase equation
  • Penta-hepta defect
  • Stability analysis

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics

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