Law of spreading of the crest of a breaking wave

In a wide range of conditions ocean waves break. This can be seen as the manifestation of a singularity in the dynamics of the fluid surface, moving under the effect of the fluid motion of the underlying fluid. We show that, for shallow water waves at the onset of breaking, the wave crest expands in the span-wise direction as the square root of time. This is first derived from a theoretical analysis and then compared with experimental findings. The agreement is excellent. We then explore another configuration where the waves are generated by a parabolic wave maker. The focusing of the initially parabolic fronts induces interferences and also breaking of the waves if their amplitude is large enough. In this case a widening of the breaking proportional to the power $3/2$ of time is expected as it follows the Huygens cusp shape.