Open AccessNonlinear Wave Statistics in a Focal Zone
Author(s) -
T. T. Janssen,
T. H. C. Herbers
Publication year - 2009
Publication title -
journal of physical oceanography
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.706
H-Index - 143
eISSN - 1520-0485
pISSN - 0022-3670
DOI - 10.1175/2009jpo4124.1
Subject(s) - rogue wave , physics , nonlinear system , gaussian , statistical physics , monte carlo method , surface wave , narrowband , statistics , optics , mathematics , quantum mechanics
In this paper, the combined effects of refraction and nonlinearity on the evolution of ocean surface wave statistics are considered and possible implications for the likelihood of extreme waves, also known as freak or rogue waves, are examined. A frequency-angular spectrum model is derived that accounts for cubic nonlinear dynamics and weak lateral homogeneity of the medium. Through Monte Carlo simulations, the evolution of wave statistics in freely developing waves, waves over an opposing shearing current, and waves refracted over an isolated topographical feature is modeled. The simulations show that freely developing, directionally spread wave fields generally maintain near-Gaussian statistics, which was also found in earlier model studies. However, the enhanced nonlinearity caused by the refractive focusing of narrowband wave fields can result locally in strongly non-Gaussian statistics and an associated increased likelihood of extreme wave events.