An analytical solution for the diffraction problem of a submerged vertical cylinder considering bottom-mounted barrier effect

Abstract

Using the methods of variable separation and eigenfunction expansion for velocity potentials, an analytical expression for the composite structure of a submerged cylinder over a coaxial, bottom-mounted cylinder in finite depth is developed. This model is also applicable for the isolated submerged truncated cylinder by careful choice of bottom cylinder height. The exciting forces on the submerged cylinder obtained by the proposed analytical solution and the boundary element method (BEM) agree well with each other, which shows good reliability of the analytical expression. Based on the proposed model, the effects of wave force on submerged cylinder owing to the existence of topographical obstacles of different sizes are investigated. The results show that various geometrical parameters of the bottom cylinder alter wave force on the upper cylinder significantly. Considering the impact of barrier, horizontal wave force and vertical wave force on submerged cylinder arrive there are several peaks at different frequencies, while the isolated cylinder always reaches the peak at a certain frequency. The peak value of wave forces may increase or decrease, but that of overturning moment has a maximum value of two to four times amplitude.