Scattering of waves by a circular disk submerged at a finite depth beneath the sea covered by an inertial surface

Using the linear water wave theory, the present study provides an analysis of water wave scattering by a horizontally submerged circular disk in a fluid of finite depth, including the simultaneous effects of an inertial surface and surface tension at the free surface. The entire fluid region is partitioned into three sub-regions and the harmonic expressions for the velocity potentials are determined by the matched eigenfunction expansion method, incorporating a modified free-surface boundary condition that accounts for surface mass density and surface tension coefficient. Variation of the wave height due to the disk and the wave load acting on the disk have been numerically studied for different values of dimensionless parameters such as the inertial surface parameter, submerged depth of the disk, the relative water depth, and the azimuthal angle of scattering. Numerical results demonstrate that the wave focusing phenomenon typically observed at the rear of the disk, as well as the resulting force coefficients, are significantly altered when surface tension and inertia are taken into account. Moreover, the presence of an inertial surface reduces wave heights and shifts the peaks of the force coefficients toward lower frequencies, while surface tension plays an active role in modifying the effective wavenumbers, particularly for shorter incident wavelengths.