Thesis (M.S. in Mechanical and Environmental Engineering)--University of California Santa Barbara, 2006. / "March 2006." Description based on title screen as viewed on June 8, 2010. DTIC Descriptor(s): Quartz, Slope, Water Erosion, Particle Size, Numerical Analysis, Equations, Theses, Sediment Transport. DTIC Identifier(s): Erosion Rates, Surface Slope, Sedflume (Ediment Erosion at Depth Flume) Includes bibliographical references (leaves 24-25). Also available in print.

A finite volume, shock-capturing scheme is used to solve the shallow water equations on unstructured triangular meshes. The conditions are characterised by: slow flow velocities (up to 1m/s), long time scale (around 10 days), and large domains (50-100km across). Systematic verification is carried out by comparing numerical with analytical results, and by comparing parameter variation in the numerical scheme with perturbation analysis, and good agreement is found. It is the first time a shock-capturing scheme has been applied to slow flows in Moreton Bay. The scheme is used to simulate transport of a pollutant in Moreton Bay, to the east of the city of Brisbane, Australia. Tidal effects are simulated using a sinusoidal time-dependent boundary condition. An advection equation is solved to model the path of a contaminant that is released in the bay, and the effect of tide and wind on the contaminant is studied. Calibration is done by comparing numerical results with measurements made at a study site in Moreton Bay. It is found that variation in the wind speed and bed friction coefficients changes the solution in the way predicted by the asymptotics. These results vary according to the shape of the bathymetry of the domain: in shallower areas, flow is more subject to shear and hence changes in wind speed or bed friction had a greater effect in adding energy to the system. The results also show that the time-dependent boundary condition reproduces the tidal effects that are found on the Queensland coast, i.e. semi-diurnal with amplitude of about 1 metre, to a reasonable degree. It is also found that the simulated path of a pollutant agrees with field measurements. The computer model means different wind speeds and directions can be tested which allows management decisions to be made about which conditions have the least damaging effect on the area.

Les problèmes étudiés dans cette thèse ont trait à la dynamique des points vortex dans deux équations pour les fluides ou superfluides bidimensionnels. La première partie est dévolue à l'équation d'Euler incompressible. Nous y analysons le système mixte Euler-points vortex, introduit par Marchioro et Pulvirenti, qui décrit l'évolution d'un tourbillon obtenu par superposition de points vortex et d'une composante plus régulière. Nous examinons diverses problématiques telles que le lien entre les points de vue lagrangien et eulérien, l'unicité, l'existence et l'expansion du support du tourbillon. La seconde partie de la thèse est consacrée à une équation de Ginzburg-Landau complexe obtenue en ajoutant un terme de dissipation à l'équation de Gross-Pitaevskii. Après avoir examiné le problème de Cauchy dans l'espace d'énergie correspondant, nous étudions la dynamique des points vortex dans le cadre de données très bien préparées. Dans un dernier temps, nous considérons un autre régime asymptotique, sans vortex, dans lequel les solutions sont des perturbations de champs constants de module égal à un. Une dynamique de type ondes amorties pour la perturbation est mise en évidence.