First Order Stochastic Lagrange Model for Asymmetric Ocean Waves

Abstract

The Gaussian linear wave model, which has been successfully used in ocean engineering for more than half a century, is well understood, and there exist both exact theory and efficient numerical algorithms for calculation of the statistical distribution of wave characteristics. It is well suited for moderate seastates and deep water conditions. One drawback, however, is its lack of realism under extreme or shallow water conditions, in particular, its symmetry. It produces waves, which are stochastically symmetric, both in the vertical and in the horizontal direction. From that point of view, the Lagrangian wave model, which describes the horizontal and vertical movements of individual water particles, is more realistic. Its stochastic properties are much less known and have not been studied until quite recently. This paper presents a version of the first order stochastic Lagrange model that is able to generate irregular waves with both crest-trough and front-back asymmetries.

Slope distribution in front-back asymmetric stochastic Lagrange time waves

“…These cited works all deal with a first-order stochastic Lagrange model that produces crest-trough statistically asymmetric, but front-back symmetric, random waves, in the sense that the slope distribution at the wave front is the mirror image of that at the rear. The front-back symmetry is clearly unrealistic, and by introducing a physically motivated correlation between horizontal movement and vertical height, Lindgren andÅberg [11] obtained a stochastic Lagrange model for space waves, i.e. waves observed at a fixed moment in time, with a realistic degree of front-back asymmetry, similar to what has been observed in wave measurements in the ocean or in wave tanks.…”

“…Lindgren andÅberg [11] have given the modification required to get the explicit slope distribution (SS) at upcrossings and downcrossings for the asymmetric space waves in the linked Lagrange model.…”

“…This will give a phase shift completely different from that in the linked model. On the other hand, the slope derivative distributions in the two-dimensional space wave depend on three different covariances related to the X-process, as shown in [11,Theorem 1], and, hence, it is not possible to calibrate the forced model to nearly the same properties as the linked model. It seems that more detailed studies of water particle velocities in real waves are needed in order to find a good correlation and transfer function structure in the asymmetric first-order Lagrange model; see the discussion in [10].…”

Exact asymmetric slope distributions in stochastic Gauss–Lagrange ocean waves

“…In a series of recent papers, [6][7][8][9][10], Lindgren statistical distributions of many individual wave characteristics, including steepness/slope, both for the space formulation (with time frozen), and the time formulation (at fixed location).…”

Investigation on the Scattering From One-Dimensional Nonlinear Fractal Sea Surface by Second-Order Small-Slope Approximation

“…A one-dimensional nonlinear fractal sea surface model has been established based on the narrow-band Lagrange model in this paper, in which the vertical and horizontal skewnesses are both considered [30][31][32]. In fact, this model has been used to study the Doppler spectrum of sea surface by Wang et al in [32], but the method used in [32] is twoscale method, which can not calculate the scattering field directly from linear and nonlinear sea surfaces.…”