Scattering of Water Waves by Two Surface-piercing Vertical Barriers

It is known that there are two infinite sets of discrete frequenciesfor which deep water waves may be either totally reflected ortotally transmitted by a pair of surface-piercing barriers ofequal length. Here the problem is further investigated usingan accurate method based on eigenfunction expansions. It isfound that for sufficiently closely spaced barriers each zeroof reflection is accompanied by a zero of transmission at anearby frequency. As the barrier spacing is increased the twolowest frequency zeros of transmission coalesce and are lost.This loss of zeros of transmission in pairs continues as thebarrier spacing is further increased. The effects of different barrier lengths and finite depth arealso considered. For barriers of different lengths the zerosof reflection no longer occur while the existence of the zerosof transmission is unaffected.