Eigenfunction expansion solution for wave diffraction from a uniform cylinder in front of a partially reflective wall

Abstract

In this work, wave diffraction from a uniform circular cylinder in front of a partially reflective wall is solved with the aid of its mirror image cylinder arranged symmetrically about the wall. The mirror image cylinder generates a scattering potential with its value being decreased by the wave reflection from the partially reflective wall. The eigenfunction expansion method is applied to solve this wave diffraction problem, and the Graf's addition theorem is applied to transform the scattering potential back from the imaginary to the original cylindrical coordinate system. Numerical simulations were carried out to examine the effects of the wave reflection of the partially reflective wall, the wave incidence direction, and the distance between the cylinder and the wall. It shows that the non-dimensional wave forces oscillate with the incident wave number, and the oscillation amplitude increases with the increasing reflection coefficient of the wall. In addition, the wave numbers at which the force peaks/troughs occur change significantly with the wave incidence angle and the distance between the cylinder and the wall.