Band gaps and localization of water waves over one-dimensional topographical bottoms

In this paper, the phenomenon of band gaps and Anderson localization of water waves over one-dimensional periodic and random bottoms is investigated by the transfer matrix method. The results indicate that the range of localization in random bottoms can be coincident with the band gaps for the corresponding periodic bottoms. Inside the gap or localization regime, a collective behavior of water waves appears. The results are also compared with acoustic and optical situations.