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Formation et dynamique de vagues en cellule de Hele-Shaw

Abstract : An experimental study of the Kelvin-Helmholtz instability between a gas and a viscous oil flowing parallel in a Hele-Shaw cell is reported. The strong shear undergoes the destabilisation of the interface and the appearance of propagative waves. The experimental study of the instability threshold shows an inertial origin whereas the linear phase velocity is purely viscous. A two-dimensionnal analysis combining the walls viscous dissipation and the inertial effects (non viscous theory of Kelvin-Helmholtz) confirms these experimental results. Moreover, the bifurcation from the stable state to the unstable state is subcritical. The different instability parameters -- as the threshold, the phase velocity or the wavelength -- increase strongly with the gap cell. Our flow being open, the study is yet completed by the determination, both experimentally and analytically, of a non linear convective/absolute transition. A characterisation of the dynamics of evolution of the waves in the non linear regime is then led through a fifth order complex Ginzburg-Landau equation, whom all the coefficients of which are determined experimentally and compared with success to the theory. From this study, a secondary instability of Eckhaus-Benjamin-Feir type is put to light. Finally, the precise analysis of the shape of the non linear and saturated waves, and especially their way of interaction, enables us to pick up similarities with solitons from a Korteweg-de Vries equation. The study of the unusual upstream/downstream asymmetry of the waves is also introduced by the realisation of a secondary experimental set-up of the wetting dynamics of a meniscus.
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https://tel.archives-ouvertes.fr/tel-00003920
Contributor : Laurent Meignin <>
Submitted on : Saturday, December 6, 2003 - 1:01:54 AM
Last modification on : Monday, December 14, 2020 - 9:52:15 AM
Long-term archiving on: : Friday, April 2, 2010 - 7:50:37 PM

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  • HAL Id : tel-00003920, version 1

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Laurent Meignin. Formation et dynamique de vagues en cellule de Hele-Shaw. Dynamique des Fluides [physics.flu-dyn]. Université Paris Sud - Paris XI, 2001. Français. ⟨tel-00003920⟩

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