Modelling Shallow-Water Waves: Truncated Hermite Models and the ShallowWave Routine

Statistical modelling of ocean waves is complicated by their nonlinearity, which leads in turn to non-Gaussian statistical behavior. While non-Gaussianity is present even in deep-water applications, its effects are especially pronounced as water depths decrease. We apply two types of wave models here: (1) local models of extreme wave heights/periods and breaking limits, and (2) random process models of the entire non-Gaussian wave surface. For the random process approach, we derive a new “truncated” Hermite model, which can reflect four moments and both upper- and lower-bound limiting values due to breaking and finite-depth effects. Results are calibrated and compared with an extensive model test series, comprising up to 23 hrs of histories across 19 seastates, at depths from 15–67m (full scale).