Laboratory observations of continuous and intermittent subharmonic edge waves

Abstract

The theoretical suggestion that subharmonic edge wave growth is inhibited by incident wave randomness is confirmed with observations in a large laboratory basin. Edge waves, gravity waves trapped near the shore by shoreline reflection and refraction, can be excited by an instability of waves normally incident from offshore. In the much-studied case of monochromatic, unidirectional incident waves, phase locking with incident waves allows continuous edge wave growth, culminating in edge waves with larger amplitudes than the incident waves. We present the first laboratory observations of edge wave excitation with random incident waves. Randomness associated with frequency and directional spread in incident waves disrupts phase locking between edge and incident waves, and subharmonic edge wave amplitudes never reach an equilibrium. Edge wave generation can be suppressed completely by relatively rapid variation of incident wave amplitude and (especially) phase. With moderate randomness, edge waves can be intermittent, with near zero amplitudes for many wave periods, followed by intervals with relatively energetic edge waves. Observed time-varying edge wave amplitudes and phases are broadly consistent with existing nonlinear perturbation theory but with significant disagreement. With both monochromatic and random incident waves, observed edge wave amplitudes are underpredicted by about a factor of ∼2, possibly owing to violation of the theoretical assumptions of weakly nonlinear and narrow-banded waves, simplified damping, and complete shoreline reflection. Intermittency will complicate detecting natural subharmonic edge waves.

Plain language summary

Edge waves travel parallel to the shoreline and are confined to shallow water. Subharmonic edge waves, with period twice that of waves incident on a beach, are studied in a large-scale wave basin with regular and (for the first time) random incident waves more representative of realistic ocean conditions. We confirm the recent theoretical finding that random incident waves can suppress edge wave excitation.