Resonant reflection of surface water waves by periodic sandbars

TLDR

Offshore sandbars parallel to a coast can form through wave‑induced mass transport in the bottom boundary layer, but effective formation requires sufficient wave reflection, a process that Bragg resonance theory has addressed only in the weak‑reflection regime and fails near resonance. This paper aims to explain how sandbars can induce strong reflection when the Bragg resonance condition is satisfied. The authors develop a strong‑reflection theory, compare it with Heathershaw’s experiments, and investigate how mean beach slope influences the resonance. The study shows that detuned or slowly modulated waves exhibit scattering that depends on whether the modulational frequency is above or below a threshold, that nonlinear effects in modulated wave groups can radiate long waves far beyond the short waves, and that ordinary breakpoint bars formed by plunging breakers can supply sufficient reflection to trigger the initial bars and enable resonant reflection for subsequent bars.

Abstract

One of the possible mechanisms of forming offshore sandbars parallel to a coast is the wave-induced mass transport in the boundary layer near the sea bottom. For this mechanism to be effective, sufficient reflection must be present so that the waves are partially standing. The main part of this paper is to explain a theory that strong reflection can be induced by the sandbars themselves, once the so-called Bragg resonance condition is met. For constant mean depth and simple harmonic waves this resonance has been studied by Davies (1982), whose theory, is however, limited to weak reflection and fails at resonance. Comparison of the strong reflection theory with Heathershaw's (1982) experiments is made. Furthermore, if the incident waves are slightly detuned or slowly modulated in time, the scattering process is found to depend critically on whether the modulational frequency lies above or below a threshold frequency. The effects of mean beach slope are also studied. In addition, it is found for periodically modulated wave groups that nonlinear effects can radiate long waves over the bars far beyond the reach of the short waves themselves. Finally it is argued that the breakpoint bar of ordinary size formed by plunging breakers can provide enough reflection to initiate the first few bars, thereby setting the stage for resonant reflection for more bars.