Correlation between individual waves in a real sea state

Abstract

The correlation between individual waves in a real sea state has a central role in existing theories of wave grouping. The attractive Kimura (1980) theory has two critical assumptions, that the sequence of individual wave heights follows a Markov process and that the joint distribution of consecutive wave heights follows a bivariate Rayleigh form. Analysis of measured water surface records suggests that sequences of individual waves can reasonably be described as a first order mixed autoregressive, moving-average or ARMA process, though a distinction among ARMA (1,0), ARMA (0,1) and ARMA (1,1) models was beyond the resolution of the data. These include the Markov or ARMA (1,0) model. The decisive detail, the joint distribution of consecutive wave heights in the sea state, was evaluated by a simulation methodology that is consistent with the Gaussian random wave model. The estimates are dependent on spectral shape and are consistently narrower and more sharply focussed at the peak than the corresponding bivariate Rayleigh estimate. The resulting predictions of run and group length statistics differ from the Kimura theory, though not by a sufficient margin to displace the Kimura theory as a pragmatic choice for wave grouping.