We consider problems based on linear water wave theory concerning the interaction
of oblique waves with horizontal cylinders in a fluid consisting of 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. The particular problems of wave scattering by a horizontal circular
cylinder in either the upper or lower layer are solved using multipole expansions.
This is a pre-print. The definitive version: LINTON, C.M. and CADBY, J.R., 2002. Scattering of oblique waves in a two-layer fluid. Journal of Fluid Mechanics, 461, pp. 343-364, is available at: http://jfm-www.damtp.cam.ac.uk/.