TRAPPED MODES AROUND FREELY FLOATING BODIES IN TWO-LAYER FLUIDS

Abstract. We consider the coupled system modeling the interaction of time-harmonic progres-sive water-waves with an array of three-dimensional freely floating obstacles in a two-layer fluid. Presenting a variational and operator formulation for the problem and a condition guaranteeing the existence of trapped waves, we give a number of examples of floating structures supporting trapped waves. We also study how the problem parameters (density ratio, obstacle dimensions, layer depths and radian frequency) influence the trapping condition. Key words. Trapped modes, linear water waves, freely floating obstacle, two-layer fluid. 1