A temporal study of wave scattering by multiple circular cylinders over a porous bed

The phenomenon of water wave scattering caused by a set of right circular cylinders immersed partially over a porous bed is explored. The Fourier–Bessel series is utilized to expand the velocity potentials, while the eigenfunction expansion method is employed to obtain the unknown coefficients in these velocity potentials. Various arrangements of multiple cylinders are considered, namely (i) two cylinders in an array, (ii) three cylinders in an array and in a triangular configuration, and (iii) four cylinders in an array and in a square arrangement. Numerical results for the horizontal force exerted on the circular cylinders are provided for various structural and porous-effect parameters. It has been found that, with fixed radii (heights) of the cylinders, the horizontal force on a cylinder decreases as the heights (radii) of the cylinders increase. To gain a deeper understanding of the evolution of the solution, the temporal simulations of the fluid flow are presented. The study demonstrates that having multiple circular cylinders kept in a staggered manner over a porous seabed leads to a substantial reduction in the amplitude of a surface wave toward the lee side zone. Furthermore, the velocity vector fields around both single and multiple circular cylinders have also been presented. It offers a visual framework for observing and interpreting the flow characteristics effectively. The setups presented in the study would be useful in designing offshore structures that reduce the effect of wave forces so that various marine operations can be undertaken safely.