Steep Sharp-Crested Gravity Waves on Deep Water

A new type of steep two-dimensional irrotational symmetric periodic gravity wave with local singular point inside the flow domain is revealed on inviscid incompressible fluid of infinite depth. The speed of fluid particles in the vicinity of the crest of these waves is greater than their phase speed. Corresponding particle trajectories provide insight into how gravity waves overturn and break.

Figure 1

The phase speed $c$ of surface gravity waves versus their steepness $A$.

Figure 2

The streamlines of the almost highest Stokes flow near the wave crest, extended outside the domain filled by fluid, in the frame of reference moving together with the wave.

Figure 3

The streamlines of the almost highest irregular flow near the wave crest, in the frame of reference moving together with the wave. The profile of the Stokes wave of the same steepness is also included for comparison.