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Theses

L'instabilité modulationnelle en présence de vent et d'un courant cisaillé uniforme

Abstract : This thesis manuscript treats about the influence of wind on modulational instability. A first part merges the works of Segur at al. which take into account viscous dissipation and Leblanc's work which deals with wind. A nonlinear Schrödinger equation is derived, with a forcing linear term which represents the result of the balance between wind forcing and dissipation. Visous dissipation is represented by Lundgren's model and the effect of wind is integrated into atmospheric pressure following Miles' model. Depth is finite. The stability of Stokes's waves is investigated, and numerical simulations are presented to illustrate the results. Some experimentations are done to confirm qualitatively these works. This first part was validated by a publication in the Journal of Fluid Mechanics~(2010). The second part studies the influence of the wind on the modulational instability by the intermediary of the vorticity whom it creates on the water at the surface. The model is simplified by the hypothesis of an unidirectional flow and a constant vorticity. The depth is still supposed finite. A non linear Schrödinger equation is derived, which takes into account this constant vorticity. The stability of the Stokes' wave is studied then in detail (instability diagram function of vorticity and depth, instability bandwidth, instability rate, etc.). It is demonstrated that a negative vorticity, beyond a certain threshold, eliminates the modulational instability independently of the depth. This second part has been submitted for publication in the journal Physics of Fluids.
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https://tel.archives-ouvertes.fr/tel-00716089
Contributor : Roland Thomas <>
Submitted on : Monday, July 9, 2012 - 8:57:44 PM
Last modification on : Thursday, January 23, 2020 - 6:22:06 PM
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Roland Thomas. L'instabilité modulationnelle en présence de vent et d'un courant cisaillé uniforme. Mécanique des fluides [physics.class-ph]. Aix-Marseille Université, 2012. Français. ⟨tel-00716089⟩

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