A New Probabilistic Wave Breaking Model for Dominant Wind-sea Waves Based on the Gaussian Field Theory

Abstract

This paper presents a novel method for obtaining the probability wave of breaking ($P_b$) of deep water, dominant wind-sea waves (that is, waves made of the energy within $\pm$30\% of the peak wave frequency) derived from Gaussian wave field theory. For a given input wave spectrum we demonstrate how it is possible to derive a joint probability density function between wave phase speed ($c$) and horizontal orbital velocity at wave crest ($u$) from which a model for $P_b$ can be obtained. A non-linear kinematic wave breaking criterion consistent with the Gaussian framework is further proposed. Our model would allow, therefore, for application of the classical wave breaking criterion (that is, wave breaking occurs if $u/c > 1$) in spectral wave models which, to the authors' knowledge, has not been done to date. Our results show that the proposed theoretical model has errors in the same order of magnitude as six other historical models when assessed using three field datasets. With optimization of the proposed model's single free parameter, it can become the best performing model for specific datasets. Although our results are promising, additional, more complete wave breaking datasets collected in the field are needed to comprehensively assess the present model, especially in regards to the dependence on phenomena such as direct wind forcing, long wave modulation and wave directionality.