Order Parameter for the Transition from Phase to Amplitude Turbulence

Abstract

The maximal conserved phase gradient is introduced as an order parameter to characterize the transition from phase- to defect-turbulence in the complex Ginzburg-Landau equation. It has a finite value in the phase-turbulent regime and decreases to zero when the transition to defect-turbulence is approached. Solutions with a non-zero phase gradient are studied via a Lyapunov analysis. The degree of "chaoticity" decreases for increasing values of the phase gradient and finally leads to stable travelling wave solutions. A modified Kuramoto-Sivashinsky equation for the phase-dynamics is able to reproduce the main features of the stable waves and to explain their origin.

11 pages letter (PS file) and 3 figures (PS files)

References in corpus (3)

• Disordered Regimes of the one-dimensional complex Ginzburg-Landau equation
• Characterization of the transition from defect- to phase-turbulence
• Rotating Rayleigh-Bénard Convection: Aspect Ratio Dependence of the Initial Bifurcations

Cited by in corpus (12)

• The World of the Complex Ginzburg-Landau Equation
• The Building Blocks of Spatiotemporal Intermittency
• Modulated Amplitude Waves and the Transition from Phase to Defect Chaos
• Modulated Amplitude Waves and Defect Formation in the One-Dimensional Complex Ginzburg-Landau Equation
• Wound-up phase turbulence in the Complex Ginzburg-Landau equation
• On the risks of using double precision in numerical simulations of spatio-temporal chaos
• Studies of Phase Turbulence in the One Dimensional Complex Ginzburg-Landau Equation
• Defect Chaos of Oscillating Hexagons in Rotating Convection
• Nonlinear Analysis of the Eckhaus Instability: Modulated Amplitude Waves and Phase Chaos with Non-zero Average Phase Gradient
• Phase chaos in the anisotropic complex Ginzburg-Landau Equation
• Stability of Oscillating Hexagons in Rotating Convection
• Hole-defect chaos in the one-dimensional complex Ginzburg-Landau equation