Propagation of water waves through finite periodic arrays of vertical cylinders

We study the transmission of water waves propagating in finite-size two-dimensional periodic structures which consist of bottom-mounted cylinders using the multiple-scattering method. Complete band gaps exist between the first and the second bands in square and triangular periodic structures, as well as one modeled on a graphite atomic lattice. We investigate the dependence of the band edges on the filling fraction. The graphite-type structure shows the band gap at a lower filling fraction than the others. Therefore, the graphite-type structure may be more suitable for practical coastal protection. We also calculate the first-order force on cylinders located along the symmetry direction.