THE INTERACTION OF WAVES WITH HORIZONTAL CYLINDERS IN 2-LAYER FLUIDS

We consider two-dimensional problems based on linear water wave theory concerning the interaction of waves with horizontal cylinders in a fl uid consisting of a layer of finite depth bounded above by a free surf ace and below by an infinite layer of fluid of greater density. For su ch a situation time-harmonic waves can propagate with two different wa venumbers K and k. In a single-layer fluid there are a number of recip rocity relations that exist connecting the various hydrodynamic quanti ties that arise. These relations are systematically extended to the tw o-fluid case. It is shown that for symmetric bodies the solutions to s cattering problems where the incident wave has wavenumber K and those where it has wavenumber k are related so that the solution to both can be found by just solving one of them. The particular problems of wave scattering by a horizontal circular cylinder in either the upper or l ower layer are then solved using multipole expansions.