Semi-analytical study of linear waves interaction with a vertical permeable cylinder of arbitrary cross-section based on perturbation theory

ABSTRACT

This paper studies linear waves incident to a vertical permeable cylinder with arbitrary cross-section based on the boundary element method and perturbation theory. Considering a near-zero thickness for the permeable media, and using Darcy's law, the governing equation for the wave incident to a porous circular cylinder is derived based on the boundary element method. Then using perturbation theory and considering a small parameter $\epsilon$ denoting the variation of cylinder radius from circular ones, the corresponding equations were expanded for non-circular cylinders. The developed method was applied to ellipse-shaped and rectangular cylinders. The wave forces and the wave strength inside the cylinder under a variety of parameters such as wavenumber, and porosity parameter were studied. One application of these research results is a better understanding of the behaviour of non-circular aquaculture cages in sea waves. According to the results, near-trapped modes can occur inside rectangular cages with small porosity parameters.

KEYWORDS:

• Porous cylinder
• non-circular cross-section
• perturbation theory
• wave force
• rectangular aquaculture cages

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

The data that support the findings of this study are openly available in Mendeley Data at http://doi.org/10.17632/j6cv53zz2z.1.