Integrating short- and long-term statistics for short-crested waves in deep and intermediate waters

The main objective of the present study is the combination of short- with long-term wave statistics in deep waters in order to achieve a more accurate description of the long-term wave climate in shallower waters. Such a description would provide vital information for many engineering applications in deep and intermediate waters, including design of coastal structures. This task can be accomplished by accumulating the statistics for all short-term sea conditions, considering the frequency of occurrence of each sea state during a certain period of years. A modification of an existing relationship has been developed aiming at achieving this purpose. More specifically, by using the relative frequencies of occurrence of the significant wave height (Hs) and mean zero-crossing wave period (Tm), measured at a specific location, as well as the short-term joint distributions of wave height (H) and period (T) associated with each sea state, the long-term joint distribution of H and T can be produced at that location in deep waters. Then, the long-term joint probability density function of Hs and Tm and the long-term joint probability function of H and T can be estimated at any intermediate water depth by considering wave directionality in deep waters and wave transformation of each individual wave, as waves propagate from the open sea towards shallower waters. Wave measurements obtained at three different locations in the Aegean (Greece) have been examined and compared. The results showed that, as waves propagate from deep to shallower waters, wave statistics differ from those in deeper waters, especially when waves become significantly depth limited. It is noted that this individual wave analysis refers to short-crested waves, thus wave directionality and refraction have been considered. However, in this approach, the nonlinear wave – wave interactions have not been taken into account.