Étude d'ondes non linéaires hydrodynamiques : approches théorique et expérimentale

Abstract : A first part is devoted to the study of the Rossby waves that appear in a rotating spherical shell representing the core of a terrestrial planet by thermal instabilities for two heating types. Internal heating is driven by radioactive sources and differential heating is driven by a difference of temperature between the internal and external frontiers. According to the Proudman-Taylor theorem, the flow depends only weakly on the axial coordinate because of the high rotation rate. Thus the 3D models can be simplified into quasi-geostrophic 2D models \textit{via} an axial integration. I present the first systematic comparison between 2D and 3D models (Simitev, U-Glasgow) for weakly nonlinear Rossby waves. In 2D the Landau equation that controls the amplitude of the critical wave is calculated. Predicted convection' amplitude and zonal flows agree rather well with the 3D results. The existence of a subcritical bifurcation is established at very low Ekman numbers with internal and differential heating; in this latter case, the Prandtl number also has to be small for the bifurcation to be subcritical. The second part is an experimental study of water flows and its first instabilities in an annular channel digged in a plate which may rotate, and which is sheared by a rotating lid. Three cases are studied: a pure shear where only the lid turns, a rapid corotation and a pure contrarotation. The onset of instability is studied with global measurements (using a video camera) and local ones (Laser Doppler Anemometry) and is characterized by spiralling waves. In the case of contrarotation, patterns localized in space and time may coexist with the waves. The comparison of these results with numerical ones (Serre, CNRS-Marseille) is done and shows a rather good agreement for the basic azimutal flow and the first instability (critical Reynolds number, wavenumber and angular frequency)
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Yannick Lebranchu. Étude d'ondes non linéaires hydrodynamiques : approches théorique et expérimentale. Autre. Institut National Polytechnique de Lorraine, 2008. Français. ⟨NNT : 2008INPL005N⟩. ⟨tel-01753039⟩

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