Instabilities of Hexagonal Patterns with Broken Chiral Symmetry

Abstract

Three coupled Ginzburg-Landau equations for hexagonal patterns with broken chiral symmetry are investigated. They are relevant for the dynamics close to onset of rotating non-Boussinesq or surface-tension-driven convection. Steady and oscillatory, long- and short-wave instabilities of the hexagons are found. For the long-wave behavior coupled phase equations are derived. Numerical simulations of the Ginzburg-Landau equations indicate bistability between spatio-temporally chaotic patterns and stable steady hexagons. The chaotic state can, however, not be described properly with the Ginzburg-Landau equations.

11 pages, 7 figures, submitted to Physica D

References in corpus (3)

• Square patterns in Rayleigh-Benard convection with rotation about a vertical axis
• Phase instabilities in hexagonal patterns
• A new instability for finite Prandtl number rotating convection with free-slip boundary conditions

Cited by in corpus (8)

• Odd Viscosity and Odd Elasticity
• Mean flow in hexagonal convection: stability and nonlinear dynamics
• Sideband Instabilities and Defects of Quasipatterns
• Whirling Hexagons and Defect Chaos in Hexagonal Non-Boussinesq Convection
• Stability of Oscillating Hexagons in Rotating Convection
• Instabilities and Spatio-temporal Chaos of Long-wave Hexagon Patterns in Rotating Marangoni Convection
• Chirality and odd mechanics in active columnar phases
• Induced defect nucleation and side-band instabilities in hexagons with rotation and mean flow