Bragg reflection of water waves due to submerged wavy plate breakwater

In this paper, the dual boundary element method (DBEM) is formulated and applied to study the reflection coefficient of a submerged, impermeable, wavy plate breakwater, which is modeled as a thin or non-thickness structure. The concept of the Bragg reflection is adapted to the design of a submerged wavy plate breakwater. The performance is more effective than the other types of horizontal plate breakwaters. In the theory, two-dimensional motion with the wave crests parallel to the submerged wavy plate and the linearized irrotational flow are assumed. The accuracy of the solution obtained using the numerical technique is demonstrated by comparing the numerical values with those obtained from experiments and with other analytical solutions. In addition, the numerical results of wave reflection for both a submerged, impermeable horizontal plate and a wavy plate breakwater are presented and discussed. The results reveal that the wavy plate is a better reflector than the single submerged, horizontal plate breakwater and that the wavy plate breakwater with a relative ripple amplitude is more effective. The numerical results also shows that when choosing a reasonable 2Lr/Lw′ (Lr: the ripple lengths, Lw′: the wavelength of the wave above the submerged plate), the reflection coefficients of the wavy plate can be controlled to approximate the total reflection.