Investigation of higher harmonics induced by periodically submerged obstacles at Bragg resonance

Abstract

To consider the interaction between higher harmonics and Bragg resonance induced by waves propagating on a periodic terrain, two-dimensional fully nonlinear numerical wave flumes have been established based on a time-domain higher-order boundary element method (HOBEM). HOBEM has been used to investigate higher harmonic waves generated over an array of submerged obstacles at Bragg resonance. It has been found that with an increase in the height of obstacles, the transmission coefficient for second-order harmonic free wave also increases initially and decreases thereafter, while the corresponding reflection coefficients continue to increase. Both transmission and reflection coefficients increase with increment in obstacle length and eventually saturate at certain values with marginal oscillation. When Bragg resonance occurs, the phenomenon of resonant reflection also takes place for the second-order locked wave, in addition to the well-recognized free waves. It has also been found that under the Bragg resonant condition, the second-order harmonic amplitude on the weather side of the bars shows the so-called "beat" and "parasitic beat" phenomena, which may increase the occurrence of extreme waves.