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

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 spatiotemporal 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 [1] extends this study to spatially non-periodic patterns observed in both annular and bounded channel.

Experimental study on thermocapillary convection of binary mixture in a shallow annular pool with radial temperature gradient

“…After a short period, most areas of the annular pool are invaded by the HTWs, but source and sink are present which are reminiscent of the boundaries of the initial patches. The similar explanation for the generation of source and sink is reported by Garnier et al [27]. The source and sink always exist and move slowly in the azimuthal direction, which agrees with one of two types reported by Burguete et al [28].…”

Size matters for nonlinear (protein) wave patterns

“…Thus, system borders force them into reflection-induced standing waves-with slight system-specific modifications. Fluid experiments [17,30] or oscillating chemical reactions guided by recent models as in [48,49] are further suitable candidates to verify our results. Pattern formation theory applied to stationary 2d patterns recently provided important insights into pattern orientation with respect to spatial inhomogeneities or confinement [28,54].…”

“…independent of system details [3,23,25]. Traveling waves near boundaries show similar fascinating spatio-temporal behavior [15,16,29,30]. However, the effects of strong confinement on nonlinear wave patterns have not yet been thoroughly examined.…”

Reflection and diffraction of internal waves analyzed with the Hilbert transform

“…In this article, we call Hilbert transform (or complex demodulation) the operation associating the complex-valued fieldŨ to the real field U. This demodulation technique has been previously used to compute local and instantaneous amplitudes, frequencies and wavenumbers [10,11,12] but, to the best of our knowledge, the present study is the first application in the context of internal gravity waves.…”