Analysis of Wave Scattering by Submerged Circular Disk

Abstract

Wave scattering over a horizontally submerged circular disk is analyzed by the linear potential wave theory. By means of the method of separation of variables, harmonic expressions of the velocity potential in terms of unknown constants are obtained in three subregions of the domain occupied by the fluid. A simple approach is employed to match these harmonic expressions at the common boundary of the subregions. The velocity potential is thus obtained, and consequently, the water‐surface elevation is determined. Variation of the wave height around the submerged disk versus the dimensionless disk radius, the relative water depth, and the submerged depth ratio of the disk to the total water depth is presented and discussed. The results show an effect of wave focusing around the rear of the disk. It is also noted that shallower‐water waves undergo more significant scattering when the ratio of the disk radius to the incident wavelength is fixed. The pattern of the wave‐height distribution is found to be closely related to the size of the disk but less dependent on the relative water depth.