Water wave diffraction by a surface-piercing floating compound porous cylinder in finite depth

Abstract

ABSTRACTThe present study deals with the hydrodynamic force due to water wave interaction with a floating compound porous cylinder in finite depth. The bottom and top of the lower cylinder and the side-wall of the upper cylinder (r=a) are impermeable. The problem is analysed under the assumption of small amplitude water wave theory. The sea-bed is considered to be flat. The velocity potentials are analytically derived in each fluid region based on separation of variables technique. The velocity potentials satisfy appropriate free surface condition, bottom boundary condition, matching conditions and Sommerfeld radiation condition at infinity. By using matching conditions along the boundaries of the regions, a system of linear equations for the unknown coefficients is derived and solved. A set of values of hydrodynamic force and wave run-up are obtained for different radii, different drafts and different porosity of the cylinder. It is observed that change in values in radii, draft and porosity have a significant effect on the hydrodynamic loads and wave run-up. We also analyse the hydrodynamic force due to different gaps between the cylinder and the sea-bed. The behaviour of hydrodynamic load is observed to be steady in the lower frequency. However, fluctuations are observed due to the resonance situation in the neighbourhood of a specific frequency. The hydrodynamic force almost vanishes at higher frequencies. Comparison is carried out with a floating compound cylinder, i.e. porous wall not considered in the cylinder. Useful agreement is observed from this comparison. It is expected that our result will be helpful in designing appropriate marine structures.