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Nonlinear dynamics of waves and modulated waves in 1D thermocapillary flows. I: General presentation and periodic solutions | | Nicolas Garnier
; Arnaud Chiffaudel
; Francois Daviaud
; Arnaud Prigent
; | | Date: |
21 Aug 2002 | | Journal: | Physica D 174 (1-4), pp 1-29 (2003) | | Subject: | Pattern Formation and Solitons | nlin.PS | | Abstract: | We present experimental results on hydrothermal traveling-waves dynamics in long and narrow 1D channels. The onset of primary traveling-wave patterns is briefly presented for different fluid heights and for annular or bounded channels, i.e., within periodic or non-periodic boundary conditions. For periodic boundary conditions, by increasing the control parameter or changing the discrete mean-wavenumber of the waves, we produce modulated waves patterns. These patterns range from stable periodic phase-solutions, due to supercritical Eckhaus instability, to spatio-temporal defect-chaos involving traveling holes and/or counter-propagating-waves competition, i.e., traveling sources and sinks. The transition from non-linearly saturated Eckhaus modulations to transient pattern-breaks by traveling holes and spatio-temporal defects is documented. Our observations are presented in the framework of coupled complex Ginzburg-Landau equations with additional fourth and fifth order terms which account for the reflection symmetry breaking at high wave-amplitude far from onset. The second part of this paper (nlin.PS/0208030) extends this study to spatially non-periodic patterns observed in both annular and bounded channel. | | Source: | arXiv, nlin.PS/0208029 | | Services: | Forum | Review | PDF | Favorites | |
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