This study investigated numerically the wave breaking effect on Bragg reflection by series submerged breakwaters. The numerical simulation was based on Reynolds-averaged Navier-Stokes equations coupled with the renormalization group turbulent model. Both non-breaking and breaking waves on the breakwaters were simulated by considering lower and higher submerged breakwaters. The wave reflection and transmission coefficients for both breaking and non-breaking waves were compared. The submerged breakwaters on both horizontal and sloping seabed were discussed. The results showed that the larger wave reflection coefficient due to Bragg reflection may reduce more wave transmission for non-breaking waves. As for the case of waves on a sloping bed, it was found that the reduction of wave transmission by the wave breaking over the submerged breakwater might be more than by Bragg reflection.


According to previous literature, Bragg resonance would be formed when the wavelength of surface waves is the even times than the spacing of adjacent artificial sand bars. Davies and Heathershaw(1984) proposed firstly that Bragg reflection in optical theory could be applied to coastal protection by artificial bars. Kirby and Anton(1990) confirmed that the appropriate arrangement of artificial sand bars could produce the Bragg reflection. The interactions of waves and series submerged breakwaters with Bragg reflection have been investigated with experiments and numerical models for many decades. Bailard et al. (1990) investigated the reflection coefficient could be larger than 0.4 if the incident wave condition is in line with Bragg reflection by experiments at Cape Canaveral Coast. Mase et al. (1995) developed a mild-slope wave equation for waves propagating over rigid and permeable rippled beds and conducted experiments for the Bragg reflection by series submerged breakwaters. Hsu et al.(2003) developed an evolution equation of mild-slope equation by the series submerged breakwaters. Tsai (2003) investigated the Bragg reflection by wave overs multiple composites of submerged breakwaters on sloping beach. Hsieh (2012) discussed the flow field characteristics on different number of artificial sand bars with Bragg reflection by numerical RANS model. Hsu et al.(2014) presented a numerical model to analyze the interaction of water wave over the series submerged breakwaters and investigated the flow field by particle image velocimetry (PIV) measurement techniques.

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