Exact asymmetric slope distributions in stochastic Gauss–Lagrange ocean waves

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.