Nonlinear dynamics of waves and modulated waves in 1D thermocapillary flows. I: General presentation and periodic solutions

DOI10.1016/S0167-2789(02)00680-2zbMath1076.76505arXivnlin/0208029OpenAlexW3098092579MaRDI QIDQ1851365

François Daviaud, Arnaud Chiffaudel, Nicolas Garnier, Arnaud Prigent

Publication date: 16 December 2002

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/nlin/0208029

zbMATH Keywords

periodic boundary conditionscoupled complex Ginzburg-Landau equationsreflection symmetry breaking

Mathematics Subject Classification ID

Experimental work for problems pertaining to fluid mechanics (76-05) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Capillarity (surface tension) for incompressible inviscid fluids (76B45) Interfacial stability and instability in hydrodynamic stability (76E17)

Related Items (5)

Reflection and diffraction of internal waves analyzed with the Hilbert transform ⋮ Stationary modulated-amplitude waves in the 1D complex Ginzburg-Landau equation ⋮ Hydrothermal waves and corotating rolls in laterally heated convection in simple liquids ⋮ Nonlinear dynamics of waves and modulated waves in 1D thermocapillary flows. II: Convective/absolute transitions ⋮ Nonlinear analysis of the Eckhaus instability: Modulated amplitude waves and phase chaos with nonzero average phase gradient

Cites Work

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• Critical properties of convective waves in a one-dimensional system
• On the Eckhaus instability for spatially periodic patterns
• Strong selection or rejection of spatially periodic patterns in degenerate bifurcations
• The Eckhaus instability for traveling waves
• Spatiotemporal chaos in the one-dimensional complex Ginzburg-Landau equation
• Sources, sinks and wavenumber selection in coupled CGL equations and experimental implications for counter-propagating wave systems
• Primary and secondary nonlinear global instability
• Nonlinear dynamics of waves and modulated waves in 1D thermocapillary flows. II: Convective/absolute transitions
• Sources and sinks in 1D traveling waves
• Nonlinear analysis of the Eckhaus instability: Modulated amplitude waves and phase chaos with nonzero average phase gradient
• Convective and absolute instabilities of fluid flows in finite geometry
• The stability of standing waves with small group velocity
• Bifurcation analysis of the Eckhaus instability
• The world of the complex Ginzburg-Landau equation
• Stability of plane wave solutions of complex Ginzburg-Landau equations
• Instabilities of dynamic thermocapillary liquid layers. Part 1. Convective instabilities
• Buoyant-thermocapillary instabilities in extended liquid layers subjected to a horizontal temperature gradient
• Instability of thermocapillary–buoyancy convection in shallow layers. Part 1. Characterization of steady and oscillatory instabilities
• Buoyant-thermocapillary instabilities of differentially heated liquid layers
• Spatiotemporal intermittency regimes of the one-dimensional complex Ginzburg-Landau equation
• Pattern formation outside of equilibrium
• The disintegration of wave trains on deep water Part 1. Theory
• Stability of a traveling roll system in a rotating disk flow
• Modulated amplitude waves and defect formation in the one-dimensional complex Ginzburg-Landau equation

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