Simulation of wave motion and wave breaking induced energy dissipation

We propose a one-equation turbulence model based on a modified closure relation for the length scale of turbulence. The proposed model is able to adequately represent the energy dissipation due to the wave breaking and does not need any criterion to a priori locate the wave breaking point and the region in which the turbulence model has to be activated. The numerical simulation of wave transformation is carried out by solving the Navier-Stokes equations expressed in an integral formulation on a time dependent curvilinear coordinate system where the vertical coordinate varies in time and vectors and tensors are represented in a Cartesian base system. The model performance is assessed by numerically reproducing a laboratory test which consists in producing the breaking of a spilling wave on a sloping beach.