Exact asymmetric slope distributions in stochastic Gauss–Lagrange ocean waves

Abstract:
The stochastic Lagrange wave model is a realistic alternative to

the Gaussian linear wave model, which has been successfully used

in ocean engineering for more than half a century. This paper

presents exact slope distributions and other characteristic

distributions at level crossings for symmetric and asymmetric

Lagrange space and time waves. These distributions are given

as expectations in a multivariate normal distribution,

and they have to be evaluated by simulation or numerical integration.

Interesting characteristic variables are: slopes obtained by

asynchronous sampling in space or time, slopes in space or time,

and horizontal particle velocity, when waves are observed when

the water level crosses a predetermined level.