Abstract
In the surface wind drift layer with constant momentum flux, two sets of the consistent surface elevation expressions with breaking and occurrence conditions for breaking are deduced from the first integrals of the energy and vortex variations and the kinetic and mathematic breaking criterions, then the expression of the surface elevation with wave breaking is established by using the Heaviside function. On the basis of the form of the sea surface elevation with wave breaking and the understanding of small slope sea waves, a triple composite function of real sea waves is presented including the functions for the breaking, weak-nonlinear and basic waves. The expression of the triple composite function and the normal distribution of basic waves are the expected theoretical model for surface elevation statistics.
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