Statistical properties of random wave groups.

Abstract

This study deals with the statistical properties of the group formation of random waves determined by the zero-up-cross method. Probability distributions about (1) the run of high waves (2) the total run (3) the run of resonant wave period are derived theoretically providing that the time series of wave height and wave period form the Markov chain. Transition probabilities are given by the 2-dimensional Rayleigh distribution for the wave height train and the 2-dimensional Weibull distribution for the wave period train. Good agreements between data and the theoretical distributions are obtained. Parameters which affect the statistical properties of the runs are discussed and the spectrum peakedness parameter for the run of wave height and the spectrum width parameter for the run of wave period are shown to be the most predominant. (from author's abstract)