In this study, we propose a new hyperbolic model with the same dispersive properties
as the classical Serre-Green-Naghdi model capable to capture the wave breaking
phenomenon. The hyperbolisation of the equations is based on taking into account the
finite character of the sound speed and thus the compressibility of the sea water. The method
therefore involves introducing acoustic energy into the system. In the case of coastal
waves, the effects of static compressibility are negligible. The resulting model is then a hyperbolic
approximation of the Serre-Green-Naghdi equations. The modelling of breaking
waves is obtained by adapting to this pseudo-compressible approach the depth-averaging
method of Large-Eddy Simulations (LES) where the small scale turbulence is modelled
by a turbulent viscosity, whereas the large scales are taken into account in the model by
an anisotropic tensor variable called enstrophy.