Wave statistics in nonlinear random sea

Abstract

The sea elevation at a fixed point is modelled as a quadratic form of a vector valued Gaussian process with arbitrary mean. An apparent wave is a part of the sea record observed between two following upcrossings of the still water level. Saddlepoint method is used to approximate the intensity $\mu(u)$, say, the sea level crosses the level $u$. The intensity is then used to estimate more complicated wave characteristics like wave period and crest height. Numerical examples are given.