A new crest height distribution for nonlinear and breaking waves in varying water depths

Abstract

The statistical distribution of zero-crossing crest heights represents a critical design input for a wide range of engineering applications. The present paper describes the development and validation of a new crest height model, suitable for application across a broad range of water depths. The purpose of this model is two-fold: first, to describe the amplifications of the largest crest heights arising due to nonlinear interactions beyond a second-order of wave steepness, and second, to incorporate the dissipative effects of wave breaking. Although these two effects act counter to each other, there is substantial evidence to suggest departures from existing models based upon weakly nonlinear second-order theory; the latter corresponding to current design practice. The proposed model has been developed on the basis of a significant collection of experimental results and a small subset of field measurements. It incorporates effects arising at different orders of nonlinearity as well as wave breaking in a compact formulation and covers a wide range of met-ocean conditions. Importantly, the new model has been independently validated against a very extensive database of experimental and field measurements. Taken together, these include effective water depths ranging from shallow water (kpd≈0.5) to deep water (kpd>3) and sea-state steepnesses covering mild, severe and extreme conditions. The new model is shown to provide a significant improvement in crest height predictions over existing methods. This is particularly evident in the steepest, most severe sea-states which inevitably form the basis of design calculations.