Wave attenuation on a floating rigid dock by multiple surface-piercing vertical thin perforated barriers

The scattering of gravity waves interacting with an array of multiple surface-piercing thin porous barriers is explored based on the hypothesis of linearized potential flow for finite water depth. The barriers are assumed to be stationed at a finite distance from each other and on the lee side of the dock. Also, it is hypothesized that the waves passing through the porous barriers follow Darcy’s law. The wave properties such as reflection and transmission coefficients, dissipation of wave energy, and horizontal wave force on the floating rigid dock are studied to check the effectiveness of different numbers of barriers and length ($H$) of barriers, their porosity, the spacing between barriers, and the distance between the last barrier and the floating rigid dock. It has been witnessed that more surface piercing barriers are obviously helpful in relieving the force due to the wave interaction with the floating rigid dock. It is noticed that implementing four perforated barriers not only reduces reflection by around 70% but also enhances wave energy dissipation by 90%, with equal size of barrier lengths being the most effective. The porous barriers are more conducive to alleviating the wave force than the rigid barriers. Additionally, it is observed that there is zero reflection when the barriers’ length is set at $H/h=0.7$ and set porosity at 1.212 (where $h$ is the water depth). On the other hand, the critical incidence angle $31.81°$ for reflection is also noticed with barriers of length $H/h=0.6$. Further, the expansion of the normalized spacing between the structures helps reflect and transmit the waves along with the dissipation of wave energy to display a periodic pattern. The free surface elevation plots certainly help to fortify the claim of having multiple barriers as a tool to mitigate the wave force on the floating dock.