Nonlinear wave interaction in coastal and open seas -- deterministic and stochastic theory

TL;DR

This paper reviews deterministic and stochastic theories of wave interactions in coastal and open seas, focusing on equations modeling water waves and their implications for sea-state analysis.

Contribution

It provides a comprehensive overview of wave interaction theories, including recent advances in stability analysis and stochastic modeling for different sea environments.

Findings

Stability of open ocean spectra to disturbances

Development of stochastic equations for nearshore waves

Comparison of deterministic and stochastic models

Abstract

We review the theory of wave interaction in finite and infinite depth. Both of these strands of water-wave research begin with the deterministic governing equations for water waves, from which simplified equations can be derived to model situations of interest, such as the mild slope and modified mild slope equations, the Zakharov equation, or the nonlinear Schr\"odinger equation. These deterministic equations yield accompanying stochastic equations for averaged quantities of the sea-state, like the spectrum or bispectrum. We discuss several of these in depth, touching on recent results about the stability of open ocean spectra to inhomogeneous disturbances, as well as new stochastic equations for the nearshore.