The interaction of waves with arrays of vertical circular cylinders

Abstract

The scattering of water waves by an array of N bottom-mounted vertical circular cylinders is solved exactly (under the assumption of linear water wave theory) using the method proposed by Spring & Monkmeyer in 1974. A major simplification to this theory has been found which makes the evaluation of quantities such as the forces on the cylinders much simpler. New formulae are given for the first and mean second-order forces together with one for the free-surface elevation in the vicinity of a particular cylinder. Comparisons are made between the exact results shown here and those generated using the approximate method of McIver & Evans (1984). The behaviour of the forces on the bodies in the long-wave limit is also examined for the special case of two cylinders with equal radii.

Evaluating wave forces on groups of three and nine cylinders using a 3D numerical wave tank

“…Linton and Evans (1990) presented a theory to evaluate the wave forces experienced by each of the N cylinders placed in an array by solving a system of N (2M + 1) unknowns, where M is order of the solution:…”

“…Spring and Monkmeyer (1974) presented a method with all the boundary conditions imposed at once to obtain a matrix equation to solve the problem. Linton and Evans (1990) improved on Spring and Monkmeyer by proposing a method based on potential theory to calculate the wave forces on each of the cylinders placed in a group. This method is employed in this paper for the comparison of numerical results in the case of multiple cylinders.…”

Water Wave Interaction by Dual Cylindrical Cylinders with Partial Porous Area

“…As regarding shallow water wave diffraction around a vertical cylinder, Isaacson [2], [3] was among the pioneers to derive analytical solutions. Under the assumptions of potential flow and linear wave theory, a semi-analytical solution is obtained by an Eigenfunction expansion approach first proposed for impermeable cylinders (Spring and Monkmeyer [4]), and latter simplified by Linton and Evans [5] for N bottom-mounted circular cylinders. Kagemoto and Yue [6] have developed another solution that is formally exact within the context of the linear theory.…”

“…The analysis method could be applied for the wave force evaluation to the array of dual cylindrical cylinders with partial porous area, which consist of an impermeable inner cylinder and a porous outer cylinder. Firstly, the results obtained from the developed numerical method are compared with ones such as Linton and Evans [5], and Wang and Ren [13] to verify the developed numerical analysis method. Moreover, the wave forces and water wave interaction on dual cylindrical cylinders with partial porous area are presented for various porosity depths, and the comparison between the impermeable cylinder and the permeable cylinder is made to examine the effects of porosity.…”

Hydrodynamic Interaction among Multiple Floating Cylinders in Both Waves and Slow Current

“…Hereafter, it is regarded as known. If the incoming waves are some kinds of regular waves with frequency w0 and incident angle j9, the unsteady potential can be expressed as ( 3 ) where co is the encountering frequency which is defined as ( 4 ) Here k0 is wave number which is the real solution of the dispersion relation ( 5 ) where g is gravity acceleration.…”