Nonlinear dynamics of waves and modulated waves in 1D thermocapillary flows. II: Convective/absolute transitions

Abstract

We present experimental results on hydrothermal waves in long and narrow 1D channels. In a bounded channel, we describe the primary and secondary instabilities leading to waves and modulated waves in terms of convective/absolute transitions. Because of on the combined effect of finite group velocity and of the presence of boundaries, the wave-patterns are non-uniform in space. We also investigate non-uniform wave-patterns observed in an annular channel in the presence of sources and sinks of hydrothermal waves. We connect our observations with the complex Ginzburg-Landau model equation in the very same way as in the first part of the paper (nlin.PS/0208029).

37 pages, 23 figures (elsart.cls + AMS extensions). Accepted in Physica D. See also companion paper "Nonlinear dynamics of waves and modulated waves in 1D thermocapillary flows. I: General presentation and periodic solutions" (nlin.PS/0208029). A version with high resolution figures is available on N.G. webpage

References in corpus (5)

• The World of the Complex Ginzburg-Landau Equation
• Modulated Amplitude Waves and Defect Formation in the One-Dimensional Complex Ginzburg-Landau Equation
• Nonlinear Analysis of the Eckhaus Instability: Modulated Amplitude Waves and Phase Chaos with Non-zero Average Phase Gradient
• Nonlinear dynamics of waves and modulated waves in 1D thermocapillary flows. I: General presentation and periodic solutions
• Convective and absolute Eckhaus instability leading to modulated waves in a finite box

Cited by in corpus (6)

• Reflexion and Diffraction of Internal Waves analyzed with the Hilbert Transform
• Doppler Effect of Nonlinear Waves and Superspirals in Oscillatory Media
• Nonlinear dynamics of waves and modulated waves in 1D thermocapillary flows. I: General presentation and periodic solutions
• Subcritical instabilities in a convective fluid layer under a quasi-1D heating
• Hole-defect chaos in the one-dimensional complex Ginzburg-Landau equation
• Pattern orientation in finite domains without boundaries