The propagation of surface water wave pulses over a topographical bottom with randomly arranged cylindrical steps is investigated by multiple scattering theory. It is shown that the waves within a certain frequency range can be localized due to the strong multiple scattering process. In the localized state, the wave intensity decreases exponentially as the transmitted distance increases. By making use of this effect, some components contained in the pulse can be filtered or inhibited by the cylinder ensemble and trapped for a relatively long period of time until dissipation.
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