On the physical constraints for the exceeding probability of deep water rogue waves

Abstract

Nearly four decades have elapsed since the first efforts to obtain a realistic narrow-banded model for extreme wave crests and heights were made, resulting in a couple dozen different exceeding probability distributions. These models reflect results of numerical simulations and storm records measured off of oil platforms, buoys and more recently satellite data. Nevertheless, no consensus has been achieved in either deterministic or operational approaches. Moreover, a minor issue with the established distributions is that they are not bounded by more than one physical limit while others are not bounded at all. Though the literature is rich in physical bounds for single waves, here we describe physical limits for the ensemble of waves that have not yet been addressed. As previous studies have shown, the exceeding probability distribution does not depend unequivocally on one sea state parameter, thus, this work supplies a combination of sea state parameters that provide guidance on the sea state influence on rogue wave occurrence. Based on specific bounds, we conjecture the dependence of the expected maximum of normalized wave heights (also known as abnormality index) and crests on the aforementioned sea-state parameters instead of the total number of waves in the wave record. Finally, we introduce a new dimensionless parameter that is capable of explaining the uneven distribution of rogue waves in the different storms pointed out by Stansell(2004).