Least upper bound distribution for nonlinear wave crests

The exact form of the statistical distribution of nonlinear wave crests is not known. This study proposes and develops a theoretical least upper bound (lub) distribution for large crest heights within the framework of second-order deep-water wave theory. The form of the lub distribution is determined by a simple but specific parameterization of second-order nonlinearities so as to satisfy the theoretical upper-bound on the sea-surface skewness. The implications and various integral properties of the proposed distribution are then examined. Subsequently, these are compared with measurements gathered during Hurricane Camille and also with simulations of the same data recently carried out by Forristall. The comparisons clearly confirm the validity and utility of the proposed lub distribution for large wave crests in deep water.