We consider, using linear water-wave theory, three-dimensional problems concerning the interaction of waves with structures in a fluid which contains a layer of finite depth bounded above by a free surface and below by an infinite layer of fluid of greater density. For such a situation time-harmonic waves can propagate with two different wavenumbers K and k. In a single-layer fluid there are a number of reciprocity relations that exist connecting the various hydrodynamic quantities that arise, and these relations are systematically extended to the two-fluid case. The particular problems of wave radiation and scattering by a submerged sphere in either the upper or lower layer are then solved using multipole expansions.
This is a pre-print. The definitive version: CADBY and LINTON, 2000. Three-dimensional water-wave scattering in two-layer fluids. Journal of Fluid Mechanics, 423: 155-173, is available at: http://jfm-www.damtp.cam.ac.uk/.