I am interested in mathematical analysis applied to key problems in fluid geophysics modelling, from the scale of waves interacting with sea ice to ocean-atmosphere interaction processes for climate modelling.
More specifically, I am interested in the problems of mathematical and numerical analysis such as
- PDEs, especially with non-local properties
- Multi-Physics coupling
- Wave propagation
- Free boundary problems especially in the context of water waves
- Fluid-floating structure interaction
- Multiscale analysis and homogeneisation especially in the context of porous media
Analysis of non-local ocean-atmosphere coupling model and fixed-point methods
I am studying an ocean/atmosphere coupling model with non-local properties. This model was built by taking into account coupling conditions corresponding to those used in numerical climate models. This is equivalent to considering the analysis of a coupling of two diffusion-type PDEs with a diffusion coefficient that depends on the trace of the solution. More specifically, I am studying the analysis of the well-posedness character of this problem (existence and uniqueness). I proposed a first approach in [Thery, 2025], which consists in treating the non-locality by fixed-point methods. I am also looking at the numerical analysis and the numerical implementation of the fixed-point method, which naturally raises the question of choosing coupling conditions to ensure convergence and guarantee a strong coupling.
Water waves and fluid-structure interactions
Since my post-doctoral years, I am interested in the general study of the interaction between water waves and floating structures, mainly for problems involving sea ice. This complex interaction mobilises different areas of solid mechanics for the analysis of structures, fluid mechanics and wave theory. I am studying the numerical analysis and modelling of water wave propagation in floating elastic plates. More precisely, I am working on the analysis of the scattering of water waves by thin floating (Kirchoff-Love) plates using numerical methods like Eigenfunction Matching Method or Wiener-Hopf technique. I am also interseted in the modelling and the numerical implementation of fracture of thin elastic plate induced by the water waves.
Multi-scale analysis and homogeneisation of thin porous layer
More recently I am intereted in the modelling and analysis of wave propagation in a porous floating layer using homogeneisation techniques.