Horseshoe-like patterns in first-order 3D random Gauss-Lagrange waves with directional spreading

Abstract

The Gauss–Lagrange model for ocean waves describes the vertical and horizontal movements of water particles as three correlated Gaussian fields. The model can produce irregular waves, asymmetric in both vertical and horizontal direction, and by judicious choice of a single skewness parameter the front–back asymmetry can be regulated to realistic values. In this paper, it is shown that this additive model for shallow waters can also produce horseshoe-like patterns around moderate to high wave crests. Such phenomena are usually analyzed and described as nonlinear interaction effects between different frequencies. The tool in the paper is a Slepian model for the three-dimensional movements conditioned on a wave crest