Evaluating Height-length Joint Distribution for the Crests of Ocean Waves

Jesper Rydén, Sylvie van Iseghem, Michel Olagnon, Igor Rychlik

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

ISSN 1403-9338
Statistical distributions for spatial wave characteristics are not easily obtained from temporal records. We present a probabilistic model which by numerical integration renders the joint density of crest amplitude and crest length for the spatial apparent waves at the crest of a temporal wave. The method needs as input a spectral representation of the sea, possibly a directional spectrum. Comparisons with experimental empirical data, obtained by application of a technique based on Fourier transformation combined with use of the dispersion relation, demonstrate a good agreement, in particular for high crests. In the paper, we also investigate the influence of directionality on the joint distribution.
Key words:
Wavelength, crest height, distribution, directional spectrum