Wave statistics in nonlinear random sea

Ulla Botelho Machado and Igor Rychlik

Centre for Mathematical Sciences
Mathematical Statistics
Lund Institute of Technology,
Lund University,

ISSN 1403-9338
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 µ (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.
Key words:
Crest distribution, non-Gaussian sea, Rice's formula, wave period and amplitude, Stokes waves