Statistical properties of wave groups in a random sea state

Abstract

Two apparently distinct approaches to the analysis of wave groups in a random sea state are described. In the first, the probabilities of the group-length G and the length of a ‘high run’ H are defined in terms of a wave envelope function p (t) . These lead naturally to expressions in terms of a single parameter that defines the spectral width. In the second approach, the sequence of wave heights is treated as a Markov chain, with a non-zero correlation only between successive waves. This leads to expressions for G and H in terms of transition probabilities p ₊ and p_. In this paper we find approximate analytic expressions for p ₊ and p _ and that show that the two approaches are roughly equivalent, to order v . Throughout the paper it is emphasized that the concept of a wave group assumes implicitly the neglect of those harmonic components that are either very short or very long compared with the peak frequency o _p . That is, some filtering of the original record is implied. For typical records of wind waves it is found that a band-pass filter with upper and lower cut-offs at 1.5 o _p and 0.5 o _p is the most suitable. Calculations are done for typical records of sea waves, and for some numerically simulated data, and there is agreement between the data and the analysis.