Hydrodynamic force and wave run-up due to diffraction of ocean water waves by a surface-piercing bottom-mounted compound partial-porous cylinder

Here we consider the case of a train of linear water waves incident on a bottom-mounted surface-piercing compound partial-porous cylinder consisting of two coaxial cylinders of which the upper cylinder is hollow with a thin porous side wall and the lower cylinder, with radius greater than that of the upper one, is rigid. Subsequently, we examine the associated hydrodynamic forces. Using linear water wave theory and eigenfunction expansion, the problem is developed in terms of suitable velocity potentials. The important boundary condition on the porous boundary is defined with the aid of Darcy's law. The matching conditions across the linear interface between successive fluid domains arising due the continuity of pressure and velocity are suitably used. Thereafter, a system of linear equations arises in terms of the unknowns solving which the hydrodynamic force and wave run-up for the compound partial-porous cylinder are calculated. Various numerical experiments show the effect of different parameters, such as porosity of the upper cylinder, draft ratio, the ratio of radii of the upper and lower cylinders and the depth of water on hydrodynamic force and wave run-up. It is observed that the wave force takes higher values corresponding to lower values of radius ratio, draft and porous coefficients. Further, for fixed values of radii, porosity and depth, the wave run-up is observed to be more when the wavenumber takes increasing values. The obtained results establish that different parameters may be suitably chosen in order to design useful ocean structures which may be installed as wave-absorbers for various activities in ocean including capturing of wave energy. Further, such structures can also act as the base of windmills installed in oceans to extract wind energy. The efficiency of the model developed is validated by comparing it with an available established result from which an excellent agreement is observed.