Wave scattering by circular arc shaped plates
Assuming the flow to be inviscid, incompressible and irrotational, the authors solve the linearized wave scattering problem for a stationary circular arc plate submerged in infinitely extended deep water with free surface. The governing equation is the two-dimensional Laplace equation for the velocity potential with boundary conditions on the free surface, at large depth and along the plate, and with a given far-field condition with unknown reflection and transmission coefficients. Two methods of solution are presented and compared to each other. The first one uses appropriate series expansions of the potential function outside and inside of the cylinder with the same radius as the circular arc plate, and requires the continuity of potential, velocity and pressure along the fluid circle arc which completes the solid circle plate to a full cylinder. The second method is a variational approximation which exactly models the behavior of the velocity potential at the tips of the plate. Based on the found solutions, the reflection and transmission abilities of such an arc plate as a water wave lens are comparatively demonstrated.
scientific article; zbMATH DE number 831939