A Third-Generation Model for Wind Waves on Slowly Varying, Unsteady, and Inhomogeneous Depths and Currents

A full discrete spectral model for propagation generation and dissipation of wind waves for arbitrary depth, current and wind fields is presented (WAVEWATCH). This model incorporates all relevant wave-current interaction mechanisms including changes of absolute frequencies due to unsteadiness of depth and currents. The model furthermore explicitly accounts for growth and decay of wave energy and for nonlinear resonant wave-wave interactions. The numerical schemes for propagation are basically second-order accurate. Effect of refraction and frequency shifts (due to unsteadiness of depth and current) are calculated on a fixed grid, also using second-order schemes. This paper focuses on the governing equations and the numerical algorithms. Furthermore some results for academic and realistic cases are presented to illustrate some features and merits of the model.