Wave loads by an oscillating water column in presence of bottom-mounted obstacle in the channel of finite width

Abstract

In the present study, we solved the problem of diffraction in water waves with consists of a pair of vertical cylinders in a channel having finite width. It consists of a partially submerged floating hollow cylinder place above a fixed coaxial bottom-mounted obstacle. With the help of matched eigenfunction expansion, channel multipole and variables separation methods, the analytical expression of potentials are obtained. Using these analytical expressions of diffracted velocity potentials, we can derive the expressions of exciting forces exerted by the cylinders. The influence of various parameters viz draft of the hollow cylinder, radius of the cylinders, the gap between the cylinders and the width of the channel walls on the exciting forces have been investigated. The results have been validated by comparing our results with available results. All the observations are validated through suitable graphs.

Diffraction problem due to water wave loads on a cylinder over a coaxial bottom-mounted barrier in a channel

“…Therefore, we have seen that a small spike behavior of the curves near trapping (Challan et al [5]). Now if we make a comparison between our present result and result given by Borah and Hassan [2], then we have seen that same observation in both results in the case of horizontal force. The difference between these two outcomes might be credited to the way that our work contains a solid cylinder in place of a hollow cylinder considered by Borah and Hassan [2].…”

“…Now if we make a comparison between our present result and result given by Borah and Hassan [2], then we have seen that same observation in both results in the case of horizontal force. The difference between these two outcomes might be credited to the way that our work contains a solid cylinder in place of a hollow cylinder considered by Borah and Hassan [2]. The significant difference in our results that we observed in peak values of horizontal force for the different radius of the barrier.…”

“…From the figure, we have seen that the curves of forces oscillating for the lower value of r 2 (for example, r 2 ≤ 0.5d), but the maximum value of the horizontal force occurs for the maximum value of r 2 . Therefore, we have seen that same behavior as given in Borah and Hassan [2] which gives the validation of our analytical result. Also, it is clear from the curves that the oscillating is occurs only at lower values of frequency as well as wave number and for maximum values of frequency, the forces almost vanish.…”

“…In [1] considered the diffraction problem of a couple of cylinders in a channel and solved the problem by using the method of image and green's function method. In [2] formulated the diffraction problem of a couple of cylinders in a channel and derived the first-order force on the cylinders in the presence of channel walls. In [3] gave the fundamental information diffraction and radiation of water waves by a cylinder in the water of finite depth.…”

Three Dimensional Radiated Water Wave with a Submerged Cylinder in Presence of Circular Plate

“…Also, in [11] formulated the problem of wave loads on a pair of the vertical cylinders and gave importance to hydrodynamic properties due to radiation and diffraction for the pair of cylinders. In [12] present the influence of a bottom obstacle on WOC in a channel.…”