Abstract
Nonlinear four-wave interactions amplify wave heights of deep-water generating extreme wave such as a freak wave. However, it is not clear the behavior of generated freak waves in deep-water shoaling to shallow water regions. In this study, a series of physical experiments and numerical simulations with several bathymetry configurations were conducted for unidirectional random waves from deep to shallow water regions. The maximum wave heights increase with an increase in kurtosis by third-order nonlinear interactions in deep water regions. The dependence of the kurtosis on the freak wave occurrence is weakened due to second-order nonlinear interactions associated with wave shoaling on the slope. Moreover, it is possible to understand the behavior of the high-order nonlinearity and the freak wave occurrence in shallow water regions if appropriate correction of the insufficient nonlinearity of more than O(e^2) to the standard Boussinesq equation are considered analytically.
Highlights
In the past two decades, the deep-water extreme wave such as a freak wave was measured and caused several severe damages to offshore structures and vessels
The characteristics of the freak wave occurrence in deep water regions were investigated through the comparison with MJ2006
The skewness is analytically represented by the second-order nonlinear interactions of LonguetHiggins (1963) and is given for deep-water random waves as μ (2) 3
Summary
In the past two decades, the deep-water extreme wave such as a freak wave was measured and caused several severe damages to offshore structures and vessels. Janssen (2003) theoretically investigated the freak wave occurrence caused by a consequence of quasi-resonant four-wave interactions in short time. He found that the quasiresonant nonlinear transfer is associated with the increase of fourth-order cumulant which is equivalent to kurtosis. He introduced Benjamin-Feir Index (BFI) to investigate the ratio of nonlinearity to frequency dispersion for the narrow-banded unidirectional waves, given by BFI = 2 ε (1)
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