The multi-layer shallow water model with free surface : treatment of the open boundaries

par Ronan Monjarret

Thèse de doctorat en Mathématiques appliquées

Sous la direction de Rémy Baraille, Florent Chazel et de Jean-Paul Vila.

Soutenue en 2014

à Toulouse 3 .

  • Titre traduit

    Le modèle d'eaux peu profondes multi-couches à surface libre : traitement des frontières ouvertes


  • Pas de résumé disponible.


  • Résumé

    This PhD dissertation, conducted as a collaboration between the SHOM and the University of Toulouse, deals with improving the treatment of open boundary conditions, for the multi-layer shallow water model with free surface. One of the main difficulties with such an objective is the determination of the modes associated to the internal surfaces liquid/liquid: the baroclinic modes. The work of this thesis focusses on two axes: The first one concerns the eigenstructure of the differential operator, associated to the general model. This allows to insure conditions of hyperbolicity and local wellposedness of the system of equations. This axis is divided in two chapters. The analysis of the two-layer model is performed in the first chapter: the calculus are exact and it is proved the gap is important compared with the single-layer model. The model with n layers, n _ 3, is studied in the second chapter: the main difficulty of these equations is the number of parameters, which obliges to concede assumptions. A new conservative multi-layer model is introduced and analyzed. The second axis deals with practical treatment of the open boundary conditions. The conditional local well-posedness of the initial-boundary value problem is proved. Afterwards, the boundary conditions are clarified for a general domain and a particular one: a rectangle. Comparison of the errors is performed between the single-layer model and the two and four-layer models, with two test case: the propagation of a gravity wave and a barotropic vortex.

Consulter en bibliothèque

La version de soutenance existe sous forme papier

Informations

  • Détails : 1 vol. (196 p.)
  • Annexes : Bibliogr. p. 189-196

Où se trouve cette thèse\u00a0?

  • Bibliothèque : Université Paul Sabatier. Bibliothèque universitaire de sciences.
  • Disponible pour le PEB
  • Cote : 2014 TOU3 0334
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