Distribution of Surface Elevations in Nonlinear Seas

Abstract

Abstract The statistical distribution describing nonlinear narrowband waves characterized with second-order nonlinearities is simplified to an explicit closed form amenable to theoretical and practical applications. The approximate form and its salient features are examined and compared with oceanic measurements in deep and shallower water depths. The approximate form developed here provides certain advantages in terms its algebraic simplicity, accuracy and a somewhat wider domain of validity, in particular, relative to a previous approximation derived from the same second-order narrowband model. Comparisons with the oceanic measurements in deep and shallow water depths also yield good agreement with the approximate form over the range of surface elevations where the second-order theory provides a relatively valid representation of nonlinear waves.