William Seez

Soutenance de thèse

In coastal zones, waves propagating at the surface of the ocean are strongly influenced by underlying shear currents. Depth-dependent velocity profiles are generated by wind blowing at the surface and friction at the bed.
Considering the Euler equations for an inviscid and incompressible fluid, along with the appropriate free-surface kinematic and dynamic boundary conditions, the effect of an underlying current on a two-dimensional progressive periodic free-surface wave of permanent form is studied. By not assuming that the velocity field derives from a scalar potential, this work extends the linear, constant vorticity, shear model to the study of arbitrary velocity profiles, both in the absence and presence of free-surface capillarity.
The chosen two-dimensional current profiles are first shown to be linearly stable in the absence of a free-surface perturbation before considering waves of arbitrary amplitude and depth. Although the wave celerity and the excess potential and kinetic energy are strongly affected by the nonlinear wave steepness parameter, the effect of vorticity is shown to be non-negligible, especially for pure gravity waves. Finally, results are presented for a linear stability analysis of these finite amplitude (2D) waves under three-dimensional perturbations. It is found that the classical classes of instability corresponding to four and five wave resonances are recovered in three-dimensions in the presence of constant or depth-dependent vorticities. Finally, a mechanism is proposed for the new dominant three-dimensional instability caused by the presence of an underlying shear current.

Jury

Didier CLAMOND - Professeur - Laboratoire J.A. Dieudonné (Université Nice Sophia-Antipolis) - Rapporteur
Miguel MANNA - Professeur - Laboratoire Charles Coulomb (Université de Montpellier II) - Rapporteur
Malek ABID - MCF, HDR - Laboratoire IRPHE (Aix-Marseille Université) - Directeur
Christian KHARIF - Professeur émérite - Laboratoire IRPHE (École Centrale Marseille) - Co-directeur
Sergey GAVRILYUK - Professeur - Laboratoire IUSTI (Aix-Marseille Université) - Examinateur
Julien TOUBOUL - MCF, HDR - Institut Méditerranéen d'Océanologie (Université de Toulon) - Examinateur