The interaction of waves with horizontal cylinders in two-layer fluids
LintonChristopher
McIverMaureen
2009
We consider two-dimensional problems based on linear water wave theory concerning
the interaction of 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. In a single-layer fluid there are a number of
reciprocity relations that exist connecting the various hydrodynamic quantities that
arise. These relations are systematically extended to the two-fluid case. It is shown
that for symmetric bodies the solutions to scattering 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
lower layer are then solved using multipole expansions.