On long-term statistics of high waves via the equivalent power storm model

The objective of this paper is to investigate the long-term statistics associated with extreme nonlinear sea wave crests. For this purpose, an equivalent power storm methodology is exploited for modeling the non-stationary time variability of the significant wave height. The method involves the identification of the real storm time histories and a subsequent replacement of each real storm by a fictitious storm that is equivalent to the real one in a statistical sense. Such an approach allows deriving the closed form expression of the return period of a nonlinear wave crest. Numerical results pertain to the calculation of this quantity starting from wave data recorded at the Gulf of Mexico and comparison with alternative methodology recommended in the practice. Next, the paper investigates effects relevant to the design of marine structures in the proximity of a coast. Specifically, the paper considers the effect of the water depth on the return values of the significant wave height and of the maximum expected crest height. The water depth influence relates to a magnification of the return values of wave crest despite the fact that the offshore significant wave height is larger than the near-shore one for a certain value of the return period, due to shoaling-refraction effects.