Boussinesq modelling of breaking waves: description of turbulence

Improved turbulent closures for use in fully nonlinear Boussinesq-type models are described here. The approach extends previous works in order to give a more flexible and accurate description of the turbulence due to a breaking wave. Turbulent stresses are handled by means of the Boussinesq hypothesis, and the eddy viscosity is assumed to vary over the water depth according to different laws. The model is described in detail, and its performances are evaluated both against available analytical solutions and against experimental data of regular waves breaking over a slope. The influence of the vertical structure of turbulence under a breaking wave is analyzed by means of four different vertical profiles of eddy viscosity; the differences in terms of hydrodynamic features are also discussed. Among the four selected profiles, two of them (the uniform one and that with uniform eddy viscosity over the top half of the water column which linearly decreases to zero over the lower half ) give better overall performances when compared with experimental data concerning velocity profiles.