Wave Kinematics at Steep Slopes: Second-Order Model

Abstract

This paper presents an experimental study investigating the relevant characteristics of the flow field induced by a regular wave acting on a uniform steep slope. Due to their uniqueness, the experimental data are of paramount importance and give a contribution toward the rational definition of wave-structure interaction. In the first part of the paper, attention is focused on the flow field characteristics, i.e., temporal and spatial behavior of surface elevation and vertical distribution of the horizontal component of the local velocity. In the second part, it is shown that the main characteristics of the velocity distributions may be represented by the variance of the distribution itself. Furthermore, it has been verified that the temporal behavior of the variance is well reproduced by a Fourier series truncated to the first three even harmonics. Relationships are presented between the coefficients of the Fourier series and some global quantities of the wave motion. Due to the relationship between the variance of velocity distribution and the momentum flux correction coefficient, the proposed second-order model allows the actual shape of the velocity profiles to be accounted for in one-dimensional numerical models describing the flow field due to the action of a wave on a steep slope.