The relation between wave asymmetry and particle orbits analysed by Slepian models

The statistical relation between ocean wave geometry and water particle movements can be formulated
in the stochastic Gauss-Lagrange model. In this paper we use Slepian models to get detailed
information of the sea surface elevation in the neighbourhood of local maxima in a Gaussian wave model and of the
movements of the top particle of the waves. We present full conditional distributions of the Gaussian
vertical and horizontal movements in the Gauss-Lagrange model, and represent them as
one regression component depending on the height and curvature at the wave maxima and
one residual component. These conditional distributions define the explicit vertical and horizontal Slepian models.

The Slepian models are used to simulate individual min-max-min waves in space,
in particular their front-back asymmetry, and the velocity vector of the particle at the wave maximum. We
find that there is a strong relation between the degree of front-back wave asymmetry and the direction of the particle
movement. We discuss the role of second order corrections to the Gaussian components and find
only minor effects for the sea states studied.

The Slepian model is shown to be an efficient tool to get detailed information about Gaussian and related models
in the neighbourhood of critical points, without the need for time and space consuming
simulations. In particular, they permit easy simulation of shape and kinematics of rare extreme waves.