I am pleased to announce that I successfully defended my Ph.D. on the 9th Sept. 2025!
Abstract. The work presented in my thesis focuses on breaking water waves. In the first part of the manuscript, a new inviscid irrotational model à la Zakharov-Craig-Sulem is motivated from Euler's free-surface equations, describing possibly overturning waves up to the splash singularity. The irrotationality being the most important hypothesis made here as it allows to use the velocity potential, the second part of the thesis aims at emphasising when this assumption is relevant in oceanic flow and when it is not. To this end, we make use of a numerical method for the free-surface Navier-Stokes equations and look for singular vorticity generation mechanisms, such as boundary layer separation.
Download the thesis
You can find below the .pdf file of my thesis, still subject to some changes for a few weeks (I am currently looking for small oversights). You can also view the slides from my defence presentation (the link opens them directly in the web browser):
Supplementary materials
Here you can find some movies/animations that could not be inserted directly in the .pdf, due to Adobe Flash Player being deprecated. Each figure number corresponds to the one in the document.
Figure 3.21 Evolution of an initially irrotational water wave of amplitude \(a = 0.5\) at \(\mathrm{Re} = 10^4\) in 3d.
Figures 4.3 and 4.5. Evolution of an initially irrotational water wave of amplitude \(a = 0.5\) at \(\mathrm{Re} = 10^6\).
Figure 5.4. An initially irrotational water wave of amplitude \(a = 0.1\) evolving above a sharp rectangular step for different values of \(\mathrm{Re}\).
Figure 5.6. Evolution of the vorticity \(\omega = \partial_x u_z - \partial_z u_x\) suring the simulation of an initially irrotational water wave of amplitude \(a = 0.1\) evolving above a sharp rectangular step with \(\mathrm{Re} = 10^5\).
Figure 5.6bis. Same as figure 5.6 but with \(\mathrm{Re} = 10^4\).
Figures 5.12(i) and 5.13. Evolution of the vorticity \(\omega = \partial_x u_z - \partial_z u_x\) suring the simulation of an initially irrotational water wave of amplitude \(a = 0.1\) evolving above a smoothed mollified step (curvature radius \(r = 0.1\)) for \(\mathrm{Re} = 10^5\).
Figure 5.12(ii). Same as figure 5.12(i) but with \(r = 0.5\).
Figure 5.12(iii). Same as figure 5.12(i) but with \(r = 1\).
Figure 5.12(iv). Same as figure 5.12(i) but with \(\mathrm{Re} = 10^4\).