A Lagrangian Model for Irregular Waves and Wave Kinematics

Abstract

It has proven difficult to describe the kinematics in irregular waves satisfactorily, in particular for the surface zone in broad-banded waves. A Lagrangian approach offers distinct advantages in this respect, eliminating the need for extrapolation of solutions or “stretching” of coordinates. This paper presents a model of irregular waves based on superposition of linear Lagrangian wave components, using an iterative method to obtain the Eulerian solution. This approach yields theoretically consistent results everywhere in the waves, and comparisons with wave flume measurements show good agreement. Also, the linear Lagrangian model includes wave interactions that would be nonlinear in an Eulerian formulation.

Exact asymmetric slope distributions in stochastic Gauss–Lagrange ocean waves

“…The free Gauss-Lagrange wave model is the stochastic version of the Miche waves, that was introduced by Gjøsund [2]. In this model, the horizontal displacement process X M (t, u) is obtained as a linear filtration of the vertical Gaussian process W (t, u) with depth and frequency dependent amplitude and phase response function…”

“…A thorough study of irregular, stochastic, Lagrange models was made by Gjøsund [2], and the theory was further developed by Socquet-Juglard et al [3] and Fouques [4]. Also Woltering and Daemrich [5] studied empirical properties of the stochastic model, based on the previous studies of regular waves.…”

Slope distribution in front-back asymmetric stochastic Lagrange time waves

“…Stochastic Lagrange models were introduced and studied by Gjøsund [7], Socquet-Juglard et al [14], and Fouques et al [5], who showed that Monte Carlo simulated stochastic Lagrange models can produce realistic crest-trough asymmetry as well as front-back asymmetry, the latter for higher-order Lagrange models. Theoretical studies of their stochastic properties have recently been made by Lindgren [9],Åberg [1], andÅberg and Lindgren [2], covering the basic stochastic properties, slope distributions at level crossings, and height distributions, respectively.…”

Slepian models for the stochastic shape of individual Lagrange sea waves

“…More recently, partial experimental studies have been made. Comparison between an additive (Miche) model and measured wave movements were reported in [5] and [6], and Fouques et al [4] extended the model to include wavelength interactions of second order. These studies show that the stochastic Lagrange model can produce both the frontback and the crest-trough asymmetry.…”

“…The Slepian models presented can be used to produce samples of individual first-order Lagrange waves, for comparison with observed waves or with data from numerical wave tanks (see [6], [4], and [21]). …”