The Intermediate Water Depth Limit of the Zakharov Equation and Consequences for Wave Prediction

• Published in: Journal of physical oceanography Vol. 37; no. 10; pp. 2389 - 2400
• Main Authors: Janssen, Peter A. E. M., Onorato, Miguel
• Format: Journal Article
• Language: English
• Published: Boston, MA American Meteorological Society 01.10.2007
• Subjects: Amplitude; Amplitudes; Approximation; Deep water; Deep-water waves; Dynamics of the ocean (upper and deep oceans); Earth, ocean, space; Energy; Energy balance; Exact sciences and technology; External geophysics; Extreme waves; Gravity waves; Intermediate water; Intermediate water masses; Marine; Physics of the oceans; Shallow water; Surface gravity waves; Surface stability; Water depth; Water waves; Wave forecasting; Wave power; Wave predicting; Finite size effect; Modulational instability; depth; Non linear process; energy transfer; Zakharov equations; Intermediate water; Wave generation; Forecast model; Shallow water; Surface gravity wave; Rogue vague
• ISSN: 0022-3670; 1520-0485
• DOI: 10.1175/JPO3128.1

Finite-amplitude deep-water waves are subject to modulational instability, which eventually can lead to the formation of extreme waves. In shallow water, finite-amplitude surface gravity waves generate a current and deviations from the mean surface elevation. This stabilizes the modulational instability, and as a consequence the process of nonlinear focusing ceases to exist when kh < 1.363. This is a well-known property of surface gravity waves. Here it is shown for the first time that the usual starting point, namely the Zakharov equation, for deriving the nonlinear source term in the energy balance equation in wave forecasting models, shares this property as well. Consequences for wave prediction are pointed out.