The Distribution Of Wave Height In Wave Groups

The distribution of wave height of ocean waves is of interest both in theory and in engineering. In ocean waves, high waves often occur with wave groups. The distribution of wave height in wave groups is of importance in areas of wave breaking and in marine engineering.Nolte derived the accumulative probability of multi-wave heights in a wave group on the basis of the linear theory of ocean waves and the Rayleigh distribution of wave height. The derivation is based on the assumption of the independence of individual wave heights in a wave group. However, observations show that the adjacent wave heights in a wave group are correlated. In this paper the wave heights in a wave group is considered as a Markov chain and the accumulative probability of multi-wave heights in a wave group is derived using one-dimensional and two-dimensional Rayleigh distribution of wave height. In comparison with Nolte's results, the results of the Markov chain model show remarkably better agreement with observations.In Nolte's study the deviation of the theoretical result from the result of observations increases with the run of the wave group. This is due to the (unjustified) assumption of the independence of individual wave heights in a wave group in Nolte's theory. In the Markov chain model, the adjacent wave heights in a wave groups are correlated. The increasing deviations of the theoretical results from the results of observations in wave groups with long runs in Nolte's theory are eliminated. So far the distributions of wave height in wave groups with different runs are considered to be identical. The Rayleigh distribution of wave height in wave groups is considered to be a valid assumption. In this paper the concept of information entropy is applied in the study of the distribution of wave height in wave groups. By analyzing wind wave data in the laboratory it is found that the run of the wave group is an important factor in influencing the distribution of wave height in wave groups. The information entropy of the distribution of wave height increases with the run of the wave group. The result indicates that the uncertainty of the wave heights increases with the run of the wave group. Non-dimensionalized with average wave height, the accumulative probability of wave height in wave groups with long runs is remarkably larger than that with short runs. This result indicates that the run of wave groups must be considered as a factor in the studies of the distribution of wave height in wave groups. It is found that the wave height distribution in wave groups depends on spectral width. The accumulative probability of wave height decreases with increasing spectral width. The effect of spectral width on the accumulative probability of wave height is comparable to that of the run. A non-dimensionalizing wave height parameter reflecting the properties of wave groups is introduced in studying the accumulative probability of wave height in wave groups. Non-dimensionalized with this parameter, the difference of the accumulative probability of wave height in wave groups with different runs can be eliminated. However, the difference of information entropy in different wave groups cannot be eliminated. The result indicates that there is intrinsic difference in wave groups with different runs. This difference cannot be eliminated by choosing different non-dimensional wave height. The distribution of individual wave height in wave groups with different runs is different.