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Here we investigate the propagation and scattering of surface water waves byarrays of bottom-mounted cylindrical steps. Both periodic and randomarrangements of the steps are considered. The wave transmission through thearrays is computed using the multiple scattering method based upon a recentlyderived formulation. For the periodic case, the results are compared to theband structure calculation. We demonstrate that complete band gaps can beobtained in such a system. Furthermore, we show that the randomization of thelocation of the steps can significantly reduce the transmission of water waves.Comparison with other systems is also discussed.Comment: 4 pages, 3 figure

Band gaps in the propagation and scattering of surface water waves over cylindrical steps