New stochastic and deterministic wave evolution models in coastal waters

Nonlinear interactions between sea waves and the sea bottom are a main mechanism for energy transfer between the different wave frequencies in the near-shore region. Nevertheless, it is difficult to implement this phenomenon in stochastic wave forecasting models due to its mathematical and physical complexity.

The existing operational formulations, while computationally efficient, do not account for many physical wave properties. The main goal of this work is derivation of a model accounting for many of these physical properties, but which also retains reasonable computational efficiency. Effects of linear and nonlinear energy dissipation, higher order bottom slopes, discretization, and ambient currents are included into the model. The results are verified against an output of nonlinear deterministic models (mild-slope and Boussinesq), laboratory experiments and field measurements.

In order to achieve sought numerical efficiency, several localized (depending only on local parameters) and partially localized (where some of the bi-spectral evolution is tracked) formulations are derived. An implementation of such a model of great importance as it allows to properly extend stochastic wave models to the nearshore region for both infra-gravity and wind-wave regimes.