The theory of the optimization provides a fascinating point of view to enhance the design and the positioning of coastal defence structures in the nearshore. We present here how we used optimization to find the best place for geotubes to fight against the erosive impact of storm waves on the Lido de Sète (Gulf of Lions).
From my work with Miguel Manna on cuspate spits, I derived an exact formulation for the growth of a tombolo, in the lee side of an artificial breakwater (picture above). This formulation relates the age of the tombolo to its size, and to parameters such as longshore diffusivity \(G0\) and wave features such as \(Hs\) or \(T01\).
From LIDAR data, wave time series and a set of aerial photos of the Gulf of Lions since the 40′, we determined fundamental relationships between wave forcings, beach features and wash-over dynamics.
Cuspate spits are typical geomorphic features (see the picture above) that develop along a shoreline affected by shallow water waves. Together with my friend Miguel Manna, we developed a full theory to understand their nucleation and their growth through time. This works combine intimately quantitative geomorphology and physics.
The Pelnard-Considère equation is a diffusion equation extensively used for the modelling of shoreline dynamics. However, it is a linear equation that cannot manage the growth of shoreline instabilities such as sand spits, cuspates,… We derive a new formalism from scratch, which introduces some kind of non-linearity and offer new striking opportunities to model shoreline features.