Extreme wave statistics of surface elevation and velocity field of gravity waves over a two-dimensional bathymetry

This paper presents the effects of two-dimensional bathymetry on the evolution of skewness and kurtosis of the surface elevation and velocity field in long-crested irregular waves propagating over a circular shoal and a submerged bar with a semicircular step. For a circular shoal, we show that the surface elevation has a local maximum of skewness and kurtosis on top of the shoal. We find that the skewness of the horizontal velocity field has similar behaviour to the surface elevation, but the kurtosis of the horizontal velocity field has two local maxima at different locations on the lee side of the shoal. For a semicircular step, which acts similar to a converging lens, we find that refraction contributes to the statistical properties of the surface elevation and horizontal velocity field to deviate from Gaussian statistics.