Phase downshift phenomenon in Bragg reflection of water waves by periodic dual-wing floating breakwaters

Abstract The study develops a numerical model based on the Boundary Element Method (BEM) to analyze Bragg reflection resulting from the interaction of surface gravity waves with a finite array of rigid dual-wing floating breakwaters (DWFBs) using small-amplitude water wave theory. The DWFBs are designed in three distinct shapes-concave, inclined, and convex-to enhance the efficiency of wave damping. The accuracy of the numerical results is validated by comparing Bragg reflection, reflection coefficients, and transmission coefficients with known results for floating box-type structures available in the literature. The findings indicate that Bragg reflection occurs consistently near 2 D / λ ≈ 1.0 ( D the distance between the centers of any two successive DWFBs and λ the wavelength of the incident wave.), regardless of the breakwater’s shape. The proposed solution effectively determines the reflection coefficient and characterizes the phase-downshift behavior associated with Bragg resonance. Additionally, the study investigates wave interactions with multiple DWFBs, revealing the mechanisms driving phase-downshift behavior. It highlights the influence of factors such as breakwater length, immersion depth, and the number of DWFBs on Bragg reflection, offering insights into optimizing breakwater design for enhanced wave attenuation.