Extreme wave statistics of random waves propagating over a 3D varying bathymetry

Non-uniform bathymetry may modify the wave statistics for both surface elevation and velocity field.
Laboratory evidence reported by Trulsen et al. (2012) shows that for a relatively long unidirectional
waves propagating over a sloping bottom, from deep to shallower water, there can be a local maximum
of kurtosis and skewness in surface elevation near the edge of the shallower side of the slope. Recent
laboratory experiments of long-crested irregular waves propagating over a shoal by Trulsen et al. (2020)
reported that the kurtosis of horizontal velocity field have different behaviour from the kurtosis of surface
elevation where the local maximum of kurtosis in surface elevation and horizontal velocity occur at
different location.
In present work, we utilize numerical simulation to study the evolution of skewness and kurtosis for
irregular waves propagating over a three-dimensional varying bathymetry. Numerical simulations are
based on High Order Spectral Method (HOSM) for variable depth as described in Gouin et al. (2017)
for wave evolution and Variational Boussinesq model (VBM) as described in Lawrence et al. (2021) for
velocity field calculation.

 

References

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LAWRENCE, C., GRAMSTAD, O. & TRULSEN, K. 2021 Variational Boussinesq model for kinematics
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TRULSEN, K., RAUSTØL, A., JORDE, S. & RYE, L. 2020 Extreme wave statistics of long-crested
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TRULSEN, K., ZENG, H. & GRAMSTAD, O. 2012 Laboratory evidence of freak waves provoked by
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