Patterns in the Waves

Abstract:

Edge waves, gravity waves trapped close to the shoreline by refraction, can in some cases form a standing wave pattern with alongshore periodic sequence of high and low runup. Nonlinear mechanisms for generation of edge waves by monochromatic waves incident on a planar beach from deep water have been elaborated theoretically and in the lab. Edge waves have been long considered a potential source for alongshore periodic morphological patterns in the swash (e.g., beach cusps), and edge-wave based predictions of cusp spacing compare qualitatively well with many field observations. We will discuss the extension of lab observations and numerical modeling to include incident waves with significant frequency and directional bandwidth. Laboratory experiments were performed at the Cantabria Coastal and Ocean Basin. The large rectangular basin (25 m cross-shore by 32 m alongshore) was heavily instrumented, had reflective sidewalls, and a steep concrete beach (slope 1:5) with a constant depth (1m) section between the wavemaker and beach. With monochromatic, normally incident waves we observed the expected, previously described subharmonic observations. Edge wave vertical heights at the shoreline reached 80cm, and edge wave uprushes exceeded the sloping beach freeboard. When frequency and frequency-directional spread are increased, the excited edge wave character changes substantially. In some cases, subharmonic excitation is suppressed completely. In other cases, edge waves are

excited intermittently and unpredictably. The spatially and temporally steady forcing required for strong, persistent subharmonic instability is lacking with even modestly spread (direction and frequency) incident waves. An SPH numerical model is capable of reproducing aspects of the observations. It seems unlikely to us that subhamonic edge waves alone are responsible for most cusp formation on natural beaches. The steady incident wave forcing needed to initiate subharmonic growth, and to maintain subharmonics long enough to build cups, are abundantly present with an incident plane wave, but lacking in many natural settings. Although subharmonic edge waves can potentially start the initial spacing, positive feedback between flow and morphology are likely critical to cusp growth.