Edge wave trapping and amplification on barred beaches

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Abstract
Theoretical predictions show that edge waves may be trapped on bars, providing a possible mechanism for bar growth. Simple solutions to the linear shallow water equations reveal that bar trapping is controlled by the depth of the water over the bar hbar and the geometry of the inshore trough relative to the bar. For specific geometries, amplification over the bar approaches an order of magnitude or more as the phase speed approaches , where amplification is defined as the surface displacement over the bar relative to the surface displacement at the shoreline. The amplification increases with the cross‐shore length scales of the profiles. The amplification is somewhat frequency dependent, generating stronger currents at the location of the bar in specific frequency ranges. Previous work showed that particular edge wave modes have the correct length scales to generate beach features such as bars and beach cusps, but field observations, notably shoreline run‐up data, frequently show no evidence of edge wave energy being concentrated at the appropriate frequencies. However, for bar‐trapped modes, edge wave energy is concentrated at the location of the bar; therefore this edge wave energy will not necessarily be evident in shoreline measurements. Strong correlation exists between the energy distribution of the longshore component of the orbital velocity observed in data collected at Superduck, October 11, 1986, and the distribution expected for a white edge wave spectrum at the shoreline. This suggests that bar‐trapped edge waves exist, in particular, at incident wave frequencies.

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