@inbook{edbf999c73874ccda91d9aace805eee6,

title = "Nonlinear Wave Interaction in Coastal and Open Seas: Deterministic and Stochastic Theory",

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{\"o}dinger 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.",

keywords = "Deep water, Kinetic equations, Mild-slope equation, Nearshore, Nonlinear interaction, Nonlinear Schr{\"o}dinger equation, Resonant interaction, Shoaling, Water waves, Wave forecasting, Zakharov equation",

author = "Raphael Stuhlmeier and Teodor Vrecica and Yaron Toledo",

note = "Publisher Copyright: {\textcopyright} 2019, Springer Nature Switzerland AG.",

year = "2019",

doi = "10.1007/978-3-030-33536-6_10",

language = "אנגלית",

isbn = "978-3-030-33535-9",

series = "Tutorials, Schools, and Workshops in the Mathematical Sciences",

publisher = "Birkhauser",

pages = "151--181",

editor = "David Henry and Konstantinos Kalimeris and P{\u a}r{\u a}u, {Emilian I.} and Jean-Marc Vanden-Broeck and Erik Wahl{\'e}n",

booktitle = "Nonlinear Water Waves",

}