Statistical properties of wave kinematics in long-crested irregular waves propagating over non-uniform bathymetry

Experimental and numerical evidence have shown that nonuniform bathymetry may alter significantly the statistical properties of surface elevation in irregular wave fields. The probability of rogue waves is increased near the edge of the upslope as long-crested irregular waves propagate into shallower water. The present paper studies the statistics of wave kinematics in long-crested irregular waves propagating over a shoal with a Monte Carlo approach. High order spectral method is employed as wave propagation model, and variational Boussinesq model is employed to calculate wave kinematics. The statistics of horizontal fluid velocity can be different from statistics in surface elevation as the waves propagate over uneven bathymetry. We notice strongly non-Gaussian statistics when the depth changes abruptly in sufficiently shallow water. We find an increase in kurtosis in the horizontal velocity around the downslope area. Furthermore, the effects of the bottom slope with different incoming waves are discussed in terms of kurtosis and skewness. Finally, we investigate the evolution of kurtosis and skewness of the horizontal velocity over a sloping bottom in a deeper regime. The vertical variation of these statistical quantities is also presented.

Automated summary

Experimental and numerical evidence suggest that nonuniform bathymetry can significantly alter the statistical properties of surface elevation in irregular wave fields. When long-crested irregular waves propagate into shallower water, the probability of rogue waves increases near the edge of the upslope. The statistics of horizontal fluid velocity differ from those of surface elevation, especially in cases of abrupt depth changes in shallow water, with non-Gaussian statistics observed.