This paper presents a novel method for obtaining the probability wave of breaking (Pb) of deep water, dominant wind‐sea waves (that is, waves made of the energy within ±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 Pb 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.

Plain Language Summary

Waves will break if the speed of the water particles on the wave crest is greater than the speed of the wave itself, causing the wave crest to overtake the front part of the wave, leading to wave breaking. Precisely simulating real ocean waves requires, therefore, a particle‐by‐particle description of the water motion, which is too expensive for the current computers to handle in real‐world applications. Instead, wave models describe waves by means of their statistical properties, that is, averaged over a large number of waves. In this paper, we present a mathematical formulation that allows to calculate the combined probability between the speed of particles on the wave crest and the wave speed based only on statistical properties. From these combined probabilities, we model the probability of wave breaking. Our results indicate that our model performed relatively well when compared to six other models using three historical datasets. Because of a lack of observed data to assess our model, we recommend that future research should focus on collecting more wave breaking data measured in the field. Future advances on this line of research could lead, for example, to improvements on operational weather forecast models.