Water wave diffraction and radiation by a vertical truncated cylinder in front of a partially reflective vertical wall

This paper studies water wave interaction with a vertical truncated cylinder in front of a partially reflective vertical wall. An analytical solution for the hydrodynamic problem is developed using the mirror image method and eigenfunction expansion method. In the outer fluid region, reduced diffracted/radiated waves induced by the mirror image of the truncated cylinder are introduced to satisfy the partially reflective condition on the vertical wall. The velocity potential of the fluid motion is expressed in the form of Bessel–Fourier series in local cylindrical coordinate systems. The expansion coefficients in the velocity potential are determined by the conditions on the cylinder surface and the boundary between adjacent regions. The wave excitation forces, added mass, and radiation damping are calculated through the velocity potential. Typical cases are presented to clarify the effect of key parameters on the hydrodynamic quantities. The results indicate that the wave excitation forces oscillate with the frequency owing to the vertical wall. The magnitude of the wall reflection coefficient mainly affects the peaks of excitation forces, whereas the phase of the reflection coefficient imposes obvious effects on the frequencies of peaks and troughs. Moreover, the added mass and radiation damping in the surge and pitch directions are more sensitive to the wall reflection coefficient (including magnitude and phase) than those in the sway and roll directions. Increasing the cylinder-wall spacing leads to more frequent oscillations of the hydrodynamic quantities, and the added mass and radiation damping in the surge and pitch directions is more susceptible to the spacing effect. Subsequently, the energy capture performance of a heave cylindrical wave energy absorber is studied based on the analytical solution. When the absorber undergoes resonance motion with water waves, its energy capture performance is significantly improved. The absorber performance at the resonant frequency increases in a nearly linear relationship with the magnitude of the reflection coefficient (with the same phase).