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Ondes non-linéaires à une et deux dimensions dans une mince couche de fluide

Abstract : Hydrothermal waves constitute an ideal nonlinear waves system which we study experimentaly the transition to spatio-temporal chaos. When the system is unidimensional, we compare an annular cell and a rectangular cell of finite extent and show that the primary instability into travelling waves occurs in the rectangular case only when the convective/absolute threshold is reached. With the same arguments, we distinguish two regimes for Eckhaus secondary instability in finite geometry: a convective and an absolute one. When the system is two-dimensional and the geometry is cylindrical, we study first the basic flow structuration, then the different instability modes depending on fluid depth and temperature difference across the cell: Archimedean spirals, targets, flowers and radial lines each appear through a supercritical Hopf bifurcation. Two hydrothermal waves modes are characterized. We present a theoretical and numerical study of the curvature effects in the two-dimensional geometry which may explain some of the differences between the two modes.
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Contributor : Nicolas Garnier <>
Submitted on : Friday, October 22, 2004 - 4:51:52 PM
Last modification on : Tuesday, November 24, 2020 - 8:45:16 AM
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  • HAL Id : tel-00007185, version 1



Nicolas B. Garnier. Ondes non-linéaires à une et deux dimensions dans une mince couche de fluide. Dynamique des Fluides [physics.flu-dyn]. Université Paris-Diderot - Paris VII, 2000. Français. ⟨tel-00007185⟩



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