Wind Wave Breaking As Clustering Point Process

Wind wave breaking plays an important role in the air-sea interaction processes.Unfortunately, because of its complicacy, lacking of proper mathematical tool, it hasmade less progress. Intermittency and randomness are the two typical characters andthus stochastic point process models would most likely suitable for breaking of windwaves. The groupness also could be described by the clustering point process.This thesis contains two parts: the first is to discuss the theory and methods forclustering process, the hypothesis and properties are also discussed, and itsstochastic inference is emphatically presented, including the clustering analysis, thetests for main process and the subsidiary process; based on a series of wind wavebreaking experiments in laboratory flume, clustering process has been established inthe second part. Under this theoretical frame, breaking rate, intermittency andgroupness of wave breaking are reinterpreted.The results from a series hypothesis tests suggest that:1) it is accepted that timeintervals between successive breaking events are mutually independent andidentically distributed, which means the main process is a renewal process andrenewal theory could be used to the study of wind wave breaking;2) most timeintervals obey gamma distribution, and the averaged breaking interval can measurethe intermittency of wave breaking. The data results also suggested a significantlinear model for the inverse of the averaged breaking interval and significantsteep and wave age;3) the number of breaking waves in a group is a propermeasure for the groupness of wave breaking and its distribution is geometric. Andstrong linearity is also exist between average cluster size and and.