On the wave height distribution of waves and wave packets around a reef lagoon of the South China Sea

Abstract

The wave height distributions of raw waves and wave packets around a reef lagoon of the South China Sea are discussed in this paper. The wave height ratio ρ=H3/m0 is used to assess how far the real wave height distribution deviates from the Rayleigh distribution. The results demonstrate a tendency for raw wave height ratios to decline with the steepness μ=kzHs when μ<0.2, where kz is the wave number referred to the mean zero-cross period Tz based on the linear dispersion relation. The connection, however, is rather shaky. On the other hand, the relative entropy εe, which describes the spectral bandwidth, appears to control the wave height ratios ρ. The variational mode decomposition approach is then used to separate the original raw waves into separate wave packets. Meanwhile, the influence of the relative entropy on ρ is eliminated. With respect to the wave packets, ρ decreases with μ. Based on observations, an empirical relationship between ρ and μ is proposed, and a modified Rayleigh distribution (MRD) is also put forward. MRD model accurately predicts the observations when H2/m0<20.