  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.
