Frozen water waves over rough topographical bottoms

The propagation of surface water waves over rough topographical bottoms is investigated by the multiple scattering theory. It is shown that the waves can be localized spatially through the process of multiple scattering and wave interference, a peculiar wave phenomenon which has been previously discussed for frozen light in optical systems [S. John, Nature 390, 661 (1997)]. This paper demonstrates that when frozen, the transmission of the waves falls off exponentially, and a cooperative behavior appears, fully supporting previous predictions. A graphic method is used to illustrate this distinct phase state in the wave propagation.