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Stabilité et dynamique d'écoulements de fluides parfaits barotropes autour d'un obstacle en présence de dispersion

Abstract : This thesis presents a series of works all dealing with extended nonlinear Hamiltonian systems including a saddle-node bifurcation. In the first part of this manuscript, we study the transition to dissipation of one-dimensional systems subjected to a local forcing and described by sine-Gordon or nonlinear Schrödinger equations (NLSE). We analytically compute the stationary states of these equations and characterize the dynamical behavior near these stationary solutions close to the bifurcation. When a gap in the dispersion relation exists, the dynamics is that of Hamiltonian systems. Conversely, when there is no gap in the dispersion relation, the dynamics of the system is coupled with the emission of sound waves that stands for an effective damping. The behavior is then typical of dissipative systems; we also show that the temporal eigenmodes undergo a spatial delocalization. The second part of this thesis is devoted to the study of two types of two-dimensional flow past an obstacle of perfect barotropic fluids: a superflow described by the NLSE and a free surface flow in the shallow water limit, with dispersive effects due to capillary forces. When the dispersive effects tend to zero, both flows have the limit of an Eulerian compressible flow with a boundary layer close to the obstacle that can be computed analytically. Using branch following methods based on pseudo-spectral methods, we calculate the bifurcation diagram of both flows. At supercritical regime, we show that in the case of the NLSE, the system starts emitting excitations, the nature of which depends on the ratio of the coherence length on the obstacle size. In the case of the shallow water flow, this emission is replaced by a finite time singularity at which dewetting occurs.
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https://tel.archives-ouvertes.fr/tel-00006825
Contributor : Chi-Tuong Pham <>
Submitted on : Monday, September 6, 2004 - 5:59:49 PM
Last modification on : Thursday, October 29, 2020 - 3:01:44 PM
Long-term archiving on: : Wednesday, September 12, 2012 - 5:40:34 PM

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  • HAL Id : tel-00006825, version 1

Citation

Chi-Tuong Pham. Stabilité et dynamique d'écoulements de fluides parfaits barotropes autour d'un obstacle en présence de dispersion. Matière Condensée [cond-mat]. Université Pierre et Marie Curie - Paris VI, 2003. Français. ⟨tel-00006825⟩

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