Comparison of linear and nonlinear extreme wave statistics

• Published in: Acta oceanologica Sinica 2016-05, Vol.35 (5), p.99-105
• Main Authors: Chalikov, Dmitry, Babanin, Alexander V.
• Format: Article
• Language: English
• Subjects: Climatology; Earth and Environmental Science; Earth Sciences; Ecology; Engineering Fluid Dynamics; Environmental Chemistry; Extreme values; Extreme waves; Freak waves; Linear waves; Marine; Marine & Freshwater Sciences; Mathematical models; Mechanics; Nonlinear waves; Oceanography; Probability theory; Two dimensional models; Wave interaction; Wave interactions; Wave statistics; Waves; 数值模拟; 极限; 波-波相互作用; 稳定性理论; 线性模式; 统计; 非线性模型; 非线性模拟
• ISSN: 0253-505X; 1869-1099
• DOI: 10.1007/s13131-016-0862-5

An extremely large（＂freak＂） wave is a typical though rare phenomenon observed in the sea. Special theories（for example, the modulation instability theory） were developed to explain mechanics and appearance of freak waves as a result of nonlinear wave-wave interactions. In this paper, it is demonstrated that the freak wave appearance can be also explained by superposition of linear modes with the realistic spectrum. The integral probability of trough-to-crest waves is calculated by two methods： the first one is based on the results of the numerical simulation of a wave field evolution performed with one-dimensional and two-dimensional nonlinear models.The second method is based on calculation of the same probability over the ensembles of wave fields constructed as a superposition of linear waves with random phases and the spectrum similar to that used in the nonlinear simulations. It is shown that the integral probabilities for nonlinear and linear cases are of the same order of values