Wave Diffraction in a Two-Layer Fluid by the Submerged Horizontal Circular Cylindrical Pipe in Front of a Cliff as a Vertical Wall

The submerged cylindrical structure in front of a cliff gets affected by the waves reflected from the cliff which behaves as a vertical wall of infinite length. This makes the hydrodynamic results different from those for the cylinder in a horizontally unbounded fluid field. We investigated the wave exciting forces on the circular cylinder when it is submerged below the interface in a density-stratified two-layer fluid, in front of the vertical wall. Employing the image principle, the present cylinder-wall problem is transformed into an equivalent imaginary physical problem of wave diffraction in an unbounded fluid domain by two identical submerged horizontal cylinders placed symmetrically concerning the vertical wall in the original problem. We solved this using the multipole expansion method and obtained infinite systems of linear algebraic equations, which are solved numerically for the unknowns by truncation. Then, the wave exciting forces on the cylinder (sway and heave forces) are solved analytically and calculated numerically. They are depicted graphically against wave numbers in several figures and have been analyzed to provide valuable results for engineering purposes.