Study Of Bragg Resonance Reflection Of Waves By Periodically Arranged Topography On Permeable Seabed

Wave Bragg resonance reflection is the phenomenon that when the wave passes through the periodic sandbar terrain,when the wavelength of the incident wave is about twice the distance between the adjacent sandbars,the wave resonates with the sandbar and causes the wave to reflect greatly.In 1982,the British scholar Davies first discovered this phenomenon,which attracted the attention and research of scholars at home and abroad.At first,the research on wave Bragg resonance reflection mainly focused on the natural sandbar terrain.In 1988,Mei introduced the concept of artificial sandbar.Since then,the academic community has begun to study the influence of artificial sandbar on wave Bragg resonance reflection.Firstly,the Bragg resonance reflection of waves on a rectangular bar on an impermeable horizontal seabed is calculated by the model.By comparing with the analytical solution of Zeng et al.,the experimental data of Hsu et al.,and the numerical solution of the extended modified mild slope equation,the convergence and correctness of the model are proved.It shows that the model can be used to study the Bragg resonance reflection of waves on a rectangular bar.At the same time,the wave height along the horizontal permeable seabed is calculated.By comparing with the Savage and Fairchild experimental data and the modified experimental results,it is proved that the model is suitable for the study of wave propagation on the permeable seabed.Then,the effects of permeability coefficient,relative width,number and immersion degree of periodically arranged bar and trench on wave Bragg resonance reflection are calculated.The calculation results show that the reflection coefficient of Bragg resonance reflection decreases with the increase of seabed permeability coefficient,increases with the increase of the number,and reaches the maximum when the relative width w/d = 0.5,regardless of the bar terrain or the trench terrain.Under the condition of bar terrain,the peak value of wave Bragg resonance reflection decreases with the increase of immersion degree,but increases under the condition of trench terrain.Compared with the case of impermeable seabed,the frequency of Bragg resonance reflection of waves is almost the same but the reflection coefficient decreases,and the zero reflection phenomenon no longer exists.Under the condition of trench terrain,the frequency of Bragg resonance reflection of waves will move to the high frequency region.This is because the water depth of the trench terrain is larger than that of the bar terrain,and the wave propagation speed becomes faster.Therefore,the wave with shorter wavelength can meet the Bragg resonance reflection condition.Then,the influence of permeability coefficient,relative width,number and other factors on wave Bragg resonance reflection under bar-trench terrain conditions is discussed,and compared with bar terrain and trench terrain.The calculation results show that,on the one hand,the wave Bragg resonance reflection caused by the bar-trench terrain and the trenchbar terrain is completely consistent;on the other hand,compared with the bar terrain and the trench terrain,the wave Bragg resonance reflection caused by the bar-trench terrain is weaker in the case of the same seabed permeability coefficient,and the same conclusion can be obtained in the same number.However,the reflection coefficient of wave Bragg resonance caused by bar-trench terrain increases with the increase of relative width,which is different from bar terrain and trench terrain.Finally,the effects of different arrangement and combination of four bar bodies and trenchs(double bar-double trench terrain,double bar-bar trench terrain,double trench-bar trench terrain)on wave Bragg resonance reflection are studied.It is found that there are double peaks in wave Bragg resonance reflection caused by double bar-double trench terrain and double bar-bar trench terrain.In summary,for all kinds of terrains arranged periodically on the permeable horizontal seabed,the Bragg resonance reflection of waves caused by bar terrain is the strongest,followed by trench terrain,and the Bragg resonance reflection of waves caused by bar and trench combination terrain is the weakest.