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Abstract
Abstract
Highlights
The Gerstner (1809) waves, with circular particle orbits, and the Miche (1944) modification to finite depth and elliptic orbits, were extended to irregular, random Lagrange waves by Pierson (1961)
In the present work the irregularity will come from a continuum of frequencies resulting in a statistical distribution for the trajectories including a statistical relation with the wave asymmetry
The theme in this paper is the relation between individual wave front–back asymmetry and the shape and orientation of water particle orbits
Summary
The Gerstner (1809) waves, with circular particle orbits, and the Miche (1944) modification to finite depth and elliptic orbits, were extended to irregular, random Lagrange waves by Pierson (1961). In this work we will use Gaussian stochastic models for the Lagrangian vertical and horizontal movements and numerically transform them to an Euler description of the water surface. We study unidirectional irregular waves developing in time and space along a straight line over constant depth h. To finish this introduction we make a comment on the photographs taken by Wallet & Ruellan (1950) on particle trajectories in plane water waves reflected by a partially absorbing barrier, reproduced in Hutter, Wang & Chubarenko (2011, figure 7.8). In the present work the irregularity will come from a continuum of frequencies resulting in a statistical distribution for the trajectories including a statistical relation with the wave asymmetry
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