Modeling of Extreme Waves

Abstract

This chapter describes the results of more than 4000 long-term (up to thousands of peak wave periods) numerical simulations of nonlinear gravity surface waves performed for the investigation of properties and estimation of statistics of extreme (‘freak’) waves. The method of solution of 2-D potential wave’s equations based on conformal mapping is applied to the simulation of wave behavior assigned by different initial conditions, defined by JONSWAP and Pierson–Moskowitz spectra. It is shown that nonlinear wave evolution sometimes results in the appearance of very big waves. There are no predictors for appearance of extreme waves; however, a height of dimensional waves is proportional to a significant wave height. The initial generation of extreme waves can occur simply as a result of linear group effects, but in some cases, the largest wave suddenly starts to grow. It is followed sometimes by a strong concentration of wave energy around a peak vertical. It is taking place typically for one peak wave period. It happens to an individual wave in a physical space, no energy exchange with surrounding waves taking place. Probability function for steep waves has been constructed. Such type function can be used for the development of operational forecast of freak waves based on a standard forecast provided by the 3-D-generation wave prediction model (WAVEWATCH or WAM).