Interaction of water waves with two closely spaced vertical obstacles

Abstract

Two-dimensional waves are incident upon a pair of vertical flat plates intersecting the free surface in a fluid of infinite depth. An asymptotic theory is developed for the resulting wave reflexion and transmission, assuming that the separation between the plates is small. The fluid motion between the plates is a uniform vertical oscillation, matched to the outer wave field by a local flow at the opening beneath the plates. It is shown that the reflexion and transmission coefficients undergo rapid changes, ranging from complete reflexion to complete transmission, in the vicinity of a critical wavenumber where the fluid column between the obstacles is resonant.