Stability of Oscillating Hexagons in Rotating Convection

Abstract

Breaking the chiral symmetry, rotation induces a secondary Hopf bifurcation in weakly nonlinear hexagon patterns which gives rise to oscillating hexagons. We study the stability of the oscillating hexagons using three coupled Ginzburg-Landau equations. Close to the bifurcation point we derive reduced equations for the amplitude of the oscillation, coupled to the phase of the underlying hexagons. Within these equation we identify two types of long-wave instabilities and study the ensuing dynamics using numerical simulations of the three coupled Ginzburg-Landau equations.

25 pages, 7 figures

References in corpus (4)

• Phase Diagram of the Two-Dimensional Complex Ginzburg-Landau Equation
• Defect Chaos of Oscillating Hexagons in Rotating Convection
• Instabilities of Hexagonal Patterns with Broken Chiral Symmetry
• A new instability for finite Prandtl number rotating convection with free-slip boundary conditions

Cited by in corpus (6)

• Odd Viscosity and Odd Elasticity
• Competition and bistability of ordered undulations and undulation chaos in inclined layer 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
• Reentrant and Whirling Hexagons in Non-Boussinesq convection