Shoreline Profile of Stokes‐Mode Edge Waves

Stokes-mode edge waves in an inviscid-fluid and irrotational-flow domain have simmlar characteristics as deep-water waves. The mathematical presentations of edge waves are identical, except the coefficients, to those of deep-water waves when the coordinate axes are rotated so that one of the axes points along the beach surface in the offshore direction. Although the similarities appear to exist in their nonlinear wave solutions, the second-harmonic component on the runup wave profile of edge waves arises from the first higher-order solution whereas, in deep-water waves, such a characteristic appears in the second higher-order solution. This early appearance of the nonlinear effect in the runup profile is due to the flow restriction caused by the beach geometry. On the other hand, the vertical water-surface displacement of edge waves has no second-harmonic component at the first-order solution, instead has the characteristic of the set-down of mean water level.