Numerical Modelling of Wind Waves. Problems, Solutions, Verifications, and Applications

The time-space evolution of the field is described by the transport equation for the 2-dimensional wave energy spectrum density, S(x,t), spread in the space, x, and time, t. This equation has the forcing named the source function, F, depending on both the wave spectrum, S, and the external wave-making factors: local wind, W(x, t), and local current, U(x, t). The source function contains certain physical mechanisms responsible for a wave spectrum evolution. It is used to distinguish three terms in function F: the wind-wave energy exchange mechanism, In; the energy conservative mechanism of nonlinear wave-wave interactions, Nl; and the wave energy loss mechanism, Dis. Differences in mathematical representation of the source function terms determine general differences between wave models. The problem is to derive analytical representations for the source function terms said above from the fundamental wave equations. Basing on publications of numerous authors and on the last two decades studies of the author, the optimized versions of the all principal terms for the source function, F, have been constructed. Detailed description of these results is presented. The final version of the source function is tested in academic test tasks and verified by implementing it into numerical shells of the well known wind wave models: WAM and WAVEWATCH. Procedures of testing and verification are presented and described in details. The superiority of the proposed new source function in accuracy and speed of calculations is shown. Finally, the directions of future developments in this topic are proposed, and some possible applications of numerical wind wave models are shown, aimed to study both the wind wave physics and global wind-wave variability at the climate scale, including mechanical energy exchange between wind, waves, and upper water layer.