Marked Point Process Model Of Wind Wave Breaking

Wind wave breaking in deep water plays an important role in the process of theair-sea interaction. It is the main source of ocean surface turbulent and the mainmechanism of limit of wave height and maintenance of wave energy dissipation of thewave field. So far there is not an appropriate mathematical model to characterize thebreaking process because of strong non-linearity and randomness of wind wavebreaking which is an important reason for difficulties and slow progress of wind wavebreaking study.Intermittent, randomness and groupness are the typical characteristics of wind wavebreaking, and random point process is a powerful tool to characterize wind wavebreaking. Breaking energy dissipation is a focus of the study of wind wave breaking.Marked point process in the random point process theory is a proper mathematicaltool to describe energy dissipation due to wind wave breaking.This thesis includes three aspects. First, a theoretical model of marked pointprocess of wind wave breaking was established. It discussed the basic assumptionsand properties which the model should satisfy. It examined in detail test methods ofindependence between marks and basic point process, which is the key to modeling. Italso examined test methods for independence identically distributed and distributionsfitting of series. In the second place, independence between marks and basic pointprocess and independence identically distributed of marks was validated based on aseries of wind wave breaking experiments, and simultaneously breaking dissipationwas considered by wave group as a unit. On the third hand, this paper also discussedthe statistical distribution of breaking energy dissipation. Finally, it investigated therelations between averaged breaking dissipation and wave field parameters, or therelations between averaged breaking dissipation and some indexes which are used tomeasure breaking frequency, such as breaking probability.The data analysis showed that:1) interval sequence is independent identicallydistributed, so the basic point process is a renewal process and the model is a marked renewal process model.2) Independence between marks and basic point process andindependence identically distributed of marks was validated. Therefore, the averagedbreaking dissipation in the unit time can be shown by the product of the averageincidence of breaking process and breaking dissipation of the average single breakingwave group.3) Breaking energy dissipation obeys mostly the lognormal distribution.This indicated that the original average breaking dissipation was not a sound indicatorwhich was used to measure the average breaking dissipation.4) There is a good linearrelationship between the average breaking dissipation and the square of significantwave height, or breaking probability.