The distribution of wave heights and periods for seas with unimodal and bimodal power density spectra

Abstract

Observed distributions of wave heights and periods taken from one year of surface wave monitoring near Martha's Vineyard are compared to distributions based on narrow-band theory. The joint distributions of wave heights and periods and the marginal height distributions are examined. The observed significant wave heights and the heights and periods of the extreme waves are also studied. Seas are classified by the shapes of their power density spectra. Spectra with a single peak are designated as unimodal and spectra with two peaks as bimodal. Seas are further classified by spectral width, a function of the three lowest spectral moments. The joint distributions of wave heights and periods from seas with narrow spectral widths take the general shape predicted by narrow-band theory and the statistics of extreme waves for these seas are well described. As spectral width increases, agreement between the theoretical and observed distributions diminishes and the significant wave heights and statistics of extreme waves show increasing variability. Bimodal seas with wide-banded spectra are found to have larger significant and extreme wave heights and shorter extreme wave periods than unimodal seas of the same width.