A wavelet-based wave group detector and predictor of extreme events over unidirectional sloping bathymetry

Extreme waves usually emerge from intensive wave groups. Detection of wave groups from random waves may be a key step in predicting the occurrence of extreme events. A new method to discriminate wave groups in random waves based on the wavelet transform is proposed and investigated. The approach can identify wave groups effectively and efficiently. To test the methods, propagation of random wave trains over constant-spanwise submerged obstacles with a wide range of bottom slopes varying from 1:3 to 1:80 are simulated using a fully nonlinear wave model. Extreme waves satisfying the definition of freak waves are identified close to the top of the obstacles. Steeper slopes increase the probability of freak waves. Moreover, it is found that the non-dimensionalized, maximum of the scaled non-uniformity wavelet power of wave groups can be used as a precursor to predict the occurrence of extreme waves over sloping bottoms. The indicator correlates linearly with the maximum heights of wave groups. Using the simulated data, formulae to predict freak waves for various wave steepness over sloping bottoms are constructed. After testing a large number of cases, it is found that the formulae predict most extreme waves successfully and effectively.