Wave trapping by freely floating obstacles in a discretely stratified fluid

Abstract

In the context of the linear water wave theory, we model the interaction of time‐harmonic water waves with an infinite array of three‐dimensional freely floating bodies in a multilayer fluid through a spectral boundary value problem, consisting of a differential equation coupled with an algebraic system. We present a variational and operator formulation for the problem and derive sufficient conditions for the existence of trapped waves. We give examples of floating obstacles supporting trapped waves in a discretely stratified fluid in different obstacle configurations with a variable number of layers. Some conclusions regarding the dependence of the sufficient condition on the number of fluid layers are drawn, considering whether the sufficient condition is of the potential or algebraic type.