Propagation of water wave over a periodically perforated bottom and the band structure

Abstract

The band structures of shallow water surface wave propagating over a periodically perforated bottom are calculated by the plane wave expansion method，and complete band gaps appear. Through considering three drilling patterns （square holes arrayed in square lattice，circular holes arrayed in square and hexagonal lattices），we find that the number，width，frequency and location of band gaps are related to the area，shape，orientation of drilled holes and the lattice. These rules are similar to those in photonic/ phononic crystals.