Wave scattering by submerged composite wavy plate breakwaters using a dual BEM

• To obtain a higher reflection and a lower transmission coefficient over a broader range of wave frequencies, a new type of suitable horizontal breakwater should be designed.
• The numerical investigation method combines the advantages provided by a single submerged horizontal plate and a sand ripple as breakwaters and presents a new type of horizontal breakwater, namely, a wavy plate breakwater, whose performance is more effective than the other types of horizontal plate breakwaters.
• The idea of dual boundary integral equations, in which a combination of the standard boundary integral equation and its derivation can be used to provide independent equations to overcome the problem of degeneracy.
• For coincident source points on the thin plate boundaries, the respective boundary integral equations are distinct, when the OBIE is applied to the source points on one of the thin plate boundaries and the HnDBIE is applied to the source point on the other.

The concept of the Bragg reflection is adapted to the design of submerged composite wavy plate breakwaters. Numerical analyses and laboratory experiments are performed to investigate the characteristics of the reflection due to submerged composite wavy plate breakwaters. The dual boundary element method (DBEM) is formulated and applied to study the impermeable composite wavy type plate breakwaters, which is modeled as a thin or zero thickness structure. The numerical method is validated by comparison with other previous published analytical solutions and reliable laboratory data of the same model. The reflection coefficients increase as the number of composite wavy plate breakwaters increases in both numerical results and laboratory measurements. In addition, the numerical results of wave reflection for a submerged, impermeable horizontal plate, a wavy plate and a composite wavy plate breakwater are presented and discussed. As expected, the performance is more effective for the composite wavy plate breakwater than for the other types of horizontal plate breakwaters. The numerical results show that when choosing a reasonable value of kh, the reflection coefficients of the composite wavy plate can be controlled to approximate the total reflection.