Evolution of extreme wave statistics in surface elevation and velocity field over a non-uniform depth

It was shown experimentally in Trulsen et al. (2012) that irregular water waves propagating over a slope may have a local maximum of kurtosis and skewness in surface elevation near the shallower side of the slope. Later on, Raustøl (2014) did laboratory experiments for irregular water waves propagating over a shoal and found the surface elevation could have a local maximum of kurtosis and skewness on top of the shoal, and a local minimum of skewness after the shoal for sufficiently shallow water. Numerical results by Sergeeva et al. (2011), Zeng & Trulsen (2012), Gramstad et al. (2013) and Viotti & Dias (2014) support the experimental results mentioned above. Just recently, Jorde (2018) did new experiment with the same shoal as in Raustøl (2014) but with additional measurement of the interior horizontal velocity. The experimental results from Raustøl (2014) and Jorde (2018) were reported in Trulsen et al. (2020) and it was found the evolution of skewness for surface elevation and horizontal velocity have the same behaviour but the kurtosis of horizontal velocity has local maximum in downslope area which is different with the kurtosis of surface elevation. In present work, we utilize numerical simulation to study the effects of incoming significant wave height, peak wave frequency on evolution of wave statistics for both surface elevation and velocity field with more general bathymetry. Numerical simulations are based on High Order Spectral Method (HOSM) for variable depth Gouin et al. (2016) for wave evolution and Variational Boussinesq model (VBM) Lawrence et al. (2018) for velocity field calculation.

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