Bragg resonance reflection of water waves by submerged triangular bars with asymmetric cross-sections

Abstract

By using the modified mild-slope equation, this paper conduct theoretical research on Bragg reflection induced by submerged triangular bars with asymmetric cross-sections. First, an analytical solution for the reflection coefficient is developed. Then the reliability of this solution is verified against previously reported results. Subsequently, the influences of the asymmetry, number, height, width, and height-to-width ratio of triangular bars on Bragg reflection are systematically analyzed via comparison with their symmetric counterparts. Results show that although the triangular bar cross-sections are inherently asymmetric, Bragg resonance can be excited provided the bars are arranged periodically. Meanwhile, the zero-reflection phenomenon occurs between adjacent resonance bands. For two mutually mirrored asymmetric cross-sections, the inclination direction of triangular bars has no effect on the reflection magnitude. Furthermore, for a specific number, height, or width of bars, cross-sectional asymmetry influences resonance intensity, but has a negligible effect on resonance frequency. For different bar numbers, the reflection coefficient curves exhibit a series of intersection points, with exactly one pair appearing between adjacent resonance bands when comparing odd and even numbers of bars. In addition, for bars with equal cross-sectional area, higher and narrower cross-sections yield stronger Bragg reflection, while the height-to-width ratio barely affects the resonance frequency.