Resonant Interactions Among Surface Water Waves

Resonant Interaction Theory (RIT)is reviewed in a variety of dynamical settings with an emphasis on the underlying approximations. The elementary interactions of three- and four-wave resonances is examined as well as deterministic and stochastic models for wavefields comprising either a broad or narrow spectrum of waves interacting in multiple and coupled sets. Some special settings in which higher-order resonances have been examined are reviewed together with Resonant Interaction Experiments (RIE) in a variety of dynamical settings with an emphasis on those aspects that are predicted. Experimental investigations on the applicability of Kelvin's dispersion relation and experiments involving gravity, gravity- capillary, and capillary wavetrains are discussed. Results from comparisons between RIT and RIE are briefly summarised and the particular absence of controlled experiments in some applications is noted.