Affiliation:
1. European Centre for Medium-Range Weather Forecasts, Reading, United Kingdom
2. Dipartimento di Fisica Generale, Università di Torino, Turin, Italy
Abstract
Abstract
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.
Publisher
American Meteorological Society
Reference24 articles.
1. Instability of periodic wavetrains in nonlinear dispersive systems.;Benjamin;Proc. Roy. Soc. London,1967
2. The desintegration of wavetrains on deep water. Part 1: Theory.;Benjamin;J. Fluid Mech.,1967
3. Stability of weakly nonlinear deep-water waves in two and three dimensions.;Crawford;J. Fluid Mech.,1981
4. On three-dimensional packets of surface waves.;Davey;Proc. Roy. Soc. London,1974
5. Three dimensional instabilities of periodic gravity waves in shallow water.;Francius;J. Fluid Mech.,2006
Cited by
90 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献