Low frequency wave resonance on fringing reefs

Reef systems have been estimated to exist along approximately 80% of the world’s coastlines with living coral reefs, relic limestone platforms and submerged rock formations being the most common types observed. The processes of wave breaking on a reef crest, setup on a reef and flow over and within a lagoon, have been the primary focus of research to date, while wave transformation shoreward of the reef crest and surf zone have also been studied. The propagation of low frequency waves has been shown to have a large influence on flow, sediment transport and morphology. Furthermore, it has been demonstrated that these waves may possess periods that, if closely correlated with the reef width and depth, may enter a standing wave type form and possibly resonate. Aim: The aim of this study was to determine the indicators of low frequency resonance in field, laboratory or numerical model data, and to identify the influence of different geometric parameters on the generation of low frequency wave resonance on a fringing reef. Methods: The indicators were tested by the use of the numerical model XBeach, which was demonstrated to consist of a numerical basis suitable for the analysis of reef systems. The model was calibrated with high-resolution field data obtained at the Ningaloo Reef (Western Australia). The tested indicators were then applied to the Ningaloo Reef field data to determine if a resonance signal could be identified at the site. Finally, a geometric parameter sensitivity analysis was conducted with an idealised reef profile based upon the Ningaloo Reef. The wave boundary of the model was forced with a JONSWAP-type spectrum that characterised the peak of a storm at the site. The influence of different geometric parameters (in both non-frictional and frictional cases) was investigated and compared to an analytical model. Results: For two time-series that are spatially lagged across a reef, three indicators need to be satisfied to demonstrate the presence of resonance. They are: the surface elevation variance across the basin must be coherent, a phase relationship associated with the mode of resonance considered must exist, and an amplification of the wave between two points considered at the frequency of resonance must occur. The results of the indicator tests showed strong agreement with a simple basin analytical model that was adapted to include the effect of a lagoon. Strong amplification (resonant) peaks were observed for the first two standing waveforms. The frequency of these peaks was affected by the setup on a reef while the amplitude was affected by the influence of friction. It was shown that for frictional values consistent with Ningaloo Reef, the amplification peaks ‘flatten’ to magnitudes similar to the progressive waves in the spectrum. The geometric sensitivity analysis indicated that the resonant frequency was more sensitive to the reef and lagoon length than the reef and lagoon depth. The amplification was greatest for the zero and first-mode of resonance. However this amplification was dampened with the introduction of friction. It was determined that resonance is not likely to occur on reef systems with the geometry, frictional characteristics and wave forcing similar to the studied section of Ningaloo Reef. Resonance may occur for reef systems with shorter reef and lagoon widths, lower frequency forcing and/or less frictional dissipation. The latter may occur for reefs that have a different roughness to Ningaloo Reef as well as for reef systems that are damaged or dying in which coral assemblages degrade into coral rubble.

Subject

resonance
fringing reef
low-frequency
XBeach
coral reef
standing wave
infragravity

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master thesis

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