Analytical solution based on BEM to oblique waves scattering by thin arc-shaped permeable barrier applied for array of aquaculture cages

Abstract

In this paper, linear oblique wave incident to a thin arc-shaped permeable barrier and an array of permeable circular cylinders was studied analytically. Two unique research objectives of this work include, considering the thickness for permeable material and the wavefield inside surrounded region by the permeable structure. The conventional boundary element method (BEM) is used to solve the governing equations of the problem. The mathematical relation between Bessel functions leads to representing the BEM-related integrals in the Fourier modes of Hankel function. This approach is useful as the singular integrals are accounted indirectly. Two basic geometries made by the permeable material are studied, including an arc-shaped and a circular geometry. The first geometry can represent a wave-breaking barrier in shallow water, while the latter can represent a floating fish farm in deep water. For the floating fish farm, the study is extended to the interaction between an array of cages. To quantify the amount of wave energy passed through the object, the Energy Transmission Index or ETI concept is introduced. ETI can be used as an indicator for permeable barriers performance.The results indicate that ETI is mostly a function of permeability rather than the wavenumber. In addition, the imaginary part of the permeability parameter plays an essential role in the problem of wave incident to permeable barrier, and it is necessary to be determined with enough accuracy. Furthermore, the shear force and bending moment on the base of the barrier and drift force and heeling moment on circular cylinders are studied. The results show, the drift force decreases as permeability and wavenumber increase. The results of this research are useful in the design of rigid circular offshore aquaculture fish cages and coastal barriers.