Skewness and asymmetry of waves are always used to describe the shape of waves and quantify nonlinearity. Parameterization of skewness and asymmetry of random waves is an efficient way to describe the wave transformation process in shallow water. However, the previous studies mainly concentrated on conditions that waves are perpendicularly propagating to shorelines, neglecting the influence of incident angles. The well-known numerical model, FUNWAVE2D, was adopted to simulate obliquely incident random waves propagating over a beach with slope 1:30. It was found that the incident angles have significant influence on the evolution of asymmetries of waves. Additionally, empirical formulae were derived to reflect the relationship between the asymmetry parameters and the local Ursell number, combining the incident angle influence.
Due to the shoaling and nonlinear effects, the shapes of gravity waves undergo significant changes in shallow water, i.e. wave crests tend to sharpen while the troughs tend to flatten with decrease of water depth. It is well known that skewness and asymmetry of near-bed velocities are directly related to sediment transport in coastal regions (Hoefel and Elgar, 2003; Gonzalez-Rodriguze and Madsen, 2007; Nielsen, 1992; Nielsen, 2006). Furthermore, the evolution of wave skewness and asymmetry is crucial to better understanding the structure failure of a coastal defence due to toe scour and the functionality of a coastal defence to protect the beach behind it from wave attack and erosions (Zou and Peng, 2011). Practically, it is difficult to measure near-bed velocities. However, Zou et al., (2003) found that near-bed velocities can be obtained by the measured surface elevations through a linear transfer function.