Since Young's (1802) double-slit experiment with optical waves, wave coherence has been studied in various scientific fields including quantum mechanics and engineering. Wave coherence happens when two intersecting waves have identical wave frequency, waveform, and constant phase difference and result in a stationary wave interference in the wavefield. Despite the importance of the subject in various scientific fields, it has not been studied broadly for the water waves. In one of the earliest studies of coherent waves, Dalrymple (1975) investigated the longshore variation of the mean water level as well as the wave height and wave-induced circulation due to the existence of intersecting waves with equal frequencies. He showed that alongshore variation of wave height due to the presence of two coherent waves results in nodal and anti-nodal points alongshore, and rip currents are formed at nodal lines with zero wave height. Following his work, Z. Wei and Dalrymple (2017) carried out numerical experiments with the Lagrangian-based smooth particle hydrodynamics (SPH) model using two intersecting waves of the same period and confirmed the
In densely populated coastal areas with sea-level rise (SLR), protecting the shorelines against erosion due to the wave impact is crucial. Along with many engineered structures like seawalls and breakwaters, there are also green structures like constructed oyster reefs (CORs) that can not only attenuate the incident waves but also grow and maintain pace with SLR. However, there is a lack of data and understanding of the long-term wave attenuation capacity of the living shoreline structures under SLR. In this study, we used the phase-resolving Boussinesq model, FUNWAVE-TVD, to examine the hydrodynamics including wave height and wave-induced currents around the CORs in the Gandys Beach living shoreline project area in the upper Delaware Bay, United States. Waves were measured at six locations (offshore to onshore, with and without CORs) in the Gandys Beach living shoreline project area for two winter months, during which four nor’easters occurred. We selected three cases that represent prevailing wind, wave, and tide conditions to examine the fine spatial and temporal changes in wave height and current velocity by the construction of the reefs. Wave heights and wave energy spectra generated from FUNWAVE-TVD were then validated with field observations. It is found that FUNWAVE-TVD is capable of simulating waves and associated hydrodynamic processes that interact with CORs. The model results show that wave attenuation rates vary with the incident wave properties and water depth, and wave-induced circulation patterns are affected by the CORs. The wave attenuation capacity of CORs over the next 100 years was simulated with the incorporation of the oyster reef optimal growth zone. Our study found that sustainable wave attenuation capacity can only be achieved when suitable habitat for COR is provided, thus it can vertically grow with SLR. Suitable habitat includes optimal intertidal inundation duration, current velocity for larval transport and settlement, on-reef oyster survival and growth, and other environmental conditions including salinity, temperature, and nutrient availability. Furthermore, the model results suggest that it would take CORs approximately 9 years after construction to reach and maintain the maximum wave attenuation capacity in sustainable living shorelines.
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