Irregular Wave Overtopping on Gravel Islands

Abstract
Gravel islands in the southern Beaufort Sea are subjected to wave activity during the short open water season. Occasional, severe storms may cause a significant amount of wave overtopping, resulting in flooding and erosion on the top of the gravel island. The statistical distributions of wave steepness, surf similarity parameter, and runup height are derived analytically using a wave‐by‐wave method. A unidirectional, irregular sea state is expressed in terms of the joint distribution of wave heights and periods proposed by a group C.N.E.X.O. The figures required for calculating the probability that runup height will exceed a selected berm height in a given sea state are presented. The expected quantity of water overtopping the berm is expressed in the form of a single integral which can be integrated numerically. Computation for a typical gravel island indicates that the probability of occurrence of wave overtopping and the expected quantity of overtopped water will increase with the spectral bandwidth an...

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