Assessment of Significant Wave Height – Peak Period Distribution Considering the Wave Steepness Limit

Abstract

The physical limit of the significant wave steepness is generally exceeded when assessing the seastate climate and the extreme iso-probability contours, i.e. too short significant wave peak periods Tp are sometimes associated to a certain significant wave height Hs. The occurrence of not physically consistent Tp is clearly due to a fault in the generally made assumption of a log-normal distribution of the Tp, where the physical limit for the period would be Tp > 0, i.e. the existence limit of the log-normal distribution, which is well below the real physical limit for significant wave steepness. If this is not a problem for pipeline design, where stability and fatigue are dominated by longer peak periods associated at each significant wave height, loads overestimation could arise for near surface structures, e.g. riser, where the largest loads and fatigue, are caused by the shorter peak periods associated to a certain significant wave height. Hence, the possibility to define a Tp distribution which respects the physical lower bound of the limiting wave steepness has a significant relevance when dealing with design and installation of near surface structures. The present paper proposes a new methodology for the assessment of the Hs-Tp distribution which respects an a-priori defined wave steepness limit. This can be done basing on the definition of significant wave steepness Sp = 2πHs/gTp2 which, assessing a limiting steepness Sp, provide an physical lower bound Tplim for the peak period Defining a new variable Tp′ = Tp – Tplim and imposing that Tp′ follows a log-normal distribution, hence having a physical limit Tp′ > 0, is equivalent to assess a Tp distribution which respects the defined significant wave steepness limit Tp > Tplim. A test case compares results obtained with the ‘old’ and ‘new’ methodologies and shows the implication on the design loads. Moreover, another test case has been investigated to verify the performance and characteristics of the new methodology.