Evolution of deep-water waves under wind forcing and wave breaking effects: Numerical simulations and experimental assessment

The evolution of two-dimensional dispersive focusing wave groups in deep water under wind forcing and wave breaking effects is investigated numerically and measurements collected from wind–wave experiments are used to evaluate the numerical simulations. Wind forcing is modeled by introducing into the dynamic boundary condition a surface slope coherent pressure distribution, which is expressed through Miles’ shear instability theory and Jeffreys’ sheltering model. To activate Jeffreys’ model in simulating waves evolving under wind forcing, an air flow separation criterion depending on wind speed and wave steepness is proposed. Direct comparisons of the measurements and the simulations are made by including the wind-driven current in the simulations. To simulate breaking waves, an eddy viscosity model is incorporated into a system of nonlinear evolution equations to dissipate wave energy and to predict surface elevation after breaking. For wave groups under no wind action, the eddy viscosity model simulates well the energy dissipation in breaking waves and predicts well the surface elevation after breaking. Under the weaker wind forcing condition, after consideration of the wind-driven current, the numerical model produces satisfying predictions. As the wind forcing becomes stronger, the disparity between the experiments and the simulations becomes more evident while the numerical results are still regarded as acceptable. The relative importances of the Miles’ and the Jeffreys’ models for waves under wind forcing are discussed through additional numerical tests.