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Ships advancing near the critical speed in a shallow channel with a randomly uneven bed



Effects of random bathymetric irregularities on wave generation by transcritical ship motion in a shallow channel are investigated. Invoking Boussinesq approximation in shallow waters, it is shown that the wave evolution is governed by an integro-differential equation combining features of Korteweg–deVries and Burgers equations. For an isolated ship, the bottom roughness weakens the transient waves radiated both fore and aft. When many ships advance in tandem, a steady mount of high water can be formed in front and a depression behind. Wave forces on both an isolated ship and a ship in a caravan are obtained as functions of the mean-square roughness, ship speed and the blockage coefficient.



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