Phase downshift or upshift of Bragg resonance for water wave reflection by an array of cycloidal bars or trenches

Abstract

For wave propagation over a finite array of cycloidal bars or trenches, an analytical solution of wave reflection in terms of Frobenius series to the modified mild-slope equation (MMSE) is given. First, the present solution related to cycloidal bars is validated against experimental data and two numerical solutions for wave reflection by rectified cosinoidal bars with the bar parameters same to those cycloidal bars, and the agreement among these solutions is quite good. Second, the present solution is compared with BEM (boundary element method) solutions to Laplace equation. It is found that the present solution is at least valid for those bars or trenches with the largest slope being not greater than 1:1. For wave reflection by cycloidal bars, the well-known phenomenon called phase downshift of Bragg resonance is confirmed again, which increases with increasing the bar height or width. For wave reflection by cycloidal trenches, it is revealed at first time that Bragg resonance always occurs at the phase with the trench distance being greater than the half incident wavelength. This new phenomenon is named as phase upshift in this paper. It is found that, the phase upshift of Bragg resonance increases with increasing the trench depth or width.