"Choppy wave" model for nonlinear gravity waves

Type Article
Date 2009-09
Language English
Author(s) Nouguier FredericORCID1, Guerin Charles-Antoine2, Chapron Bertrand3
Affiliation(s) 1 : Univ Paul Cezanne, Fac St Jerome, Inst Fresnel, UMR 6133,CNRS, F-13397 Marseille 20, France.
2 : Univ Sud Toulon Var, LSEET, UMR 6017, CNRS, F-83957 La Garde, France.
3 : IFREMER, Lab Oceanog Spatiale, F-29280 Plouzane, France.
Source Journal of Geophysical Research ( JGR ) - Oceans (0148-0227) (American Geophysical Union), 2009-09 , Vol. 114 , N. C09012 , P. 1-16
DOI 10.1029/2008JC004984
WOS© Times Cited 28
Keyword(s) sea surface statistics, nonlinear gravity waves
Abstract We investigate the statistical properties of a three-dimensional simple and versatile model for weakly nonlinear gravity waves in infinite depth, referred to as the "choppy wave model" (CWM). This model is analytically tractable, numerically efficient, and robust to the inclusion of high frequencies. It is based on horizontal rather than vertical local displacement of a linear surface and is a priori not restricted to large wavelengths. Under the assumption of space and time stationarity, we establish the complete first- and second-order statistical properties of surface random elevations and slopes for long-crested as well as fully two-dimensional surfaces, and we provide some characteristics of the surface variation rate and frequency spectrum. We establish a relationship between the so-called "dressed spectrum," which is the enriched wave number spectrum of the nonlinear surface, and the "undressed" one, which is the spectrum of the underlying linear surface. The obtained results compare favorably with other classical analytical nonlinear theories. The slope statistics are further found to exhibit non-Gaussian peakedness characteristics. Compared to observations, the measured non-Gaussian omnidirectional slope statistics can only be explained by non-Gaussian effects and are consistently approached by the CWM.
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