Wave asymmetry and particle orbits in irregular wave models

Water particle orbits are key elements in the Lagrange wave formulation. The stochastic Miche implementation of the Lagrange model is a linear Gaussian two-dimensional or three-dimensional space-time model which exhibits typical nonlinear wave characteristics when transformed to Eulerian coordinates. This paper investigates the statistical relation between the degree of front-back asymmetry of individual waves and the orbit orientation for the particle located at the wave maximum at the point of observation. It is shown that, in the Lagrangian model with statistical front-back symmetry, for individual waves there is a clear connexion between the degree of individual wave asymmetry and the orientation of the randomly deformed elliptic orbit: a steep front correlates with upward tilt, a steep back is correlated with a downward tilt. This holds both for waves observed in time and in space, and the dependence is stronger for large amplitude waves than for smaller ones. The dependence is strongly dependent on the depth and on the significant steepness and spectral width. Inclusion of the average Stokes drift has a moderate effect on the dependence. For models with forced front-back asymmetry there is both a systematic dependence and a statistical correlation between asymmetry and tilt; for large amplitude waves the systematic relation dominates. The conclusions are based on Fourier simulations of Gauss-Lagrange waves of first and second order with a wind-sea Pierson-Moskowitz spectrum and a narrow swell JONSWAP spectrum