Résumé
For the design and the construction of the defence structures against beach erosion, there is a need to predict and to understand the evolution in time of the shape of the sea sandy bed, using different numerical models and control theories. In the present paper a numerical model based on shallow water equations, which is an application of control theory to the evolution of sandy bed, is used in order to propose a formulation for the wave motion based on fluid and structure coupling, using minimization principles. Furthermore, measurements from a physical experiment are used in order to verify the accuracy of the model. The experiment was carried out in a multi directional wave basin at the SOGREAH (LHF facility, G-INP, France) and provided extensive measurements and detailed analysis of combined hydrodynamics and morphodynamics, suggesting a subtle interplay between several feedback mechanisms associated to wavedriven rip current circulations, wave nonlinearities, sediment transport, and the seabed evolution. Using the numerical model, wave characteristics and depth profiles have been calculated and compared to experimental results.