Wash waves generated by ship moving across a depth change

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Unsteady wash waves generated by a ship with constant speed moving across an uneven bottom topography is investigated by numerical simulations based on a Mixed Euler–Lagrange (MEL) method. The transition is accomplished by the ship traveling from the deep water into shallow water via a step bottom. A small tsunami would be created after this transition. However, the unsteady wave-making resistance induced by this new phenomenon has not been well documented by literature. Therefore, the main purpose of the present study is to quantify the effects of an uneven bottom on the unsteady wash waves and wave-making resistance acting on the ship. An upwind differential scheme is commonly used in the Euler method to deal with the convection terms on free-surface condition to prevent waves in upstream. Evidently, it cannot be applied to the present problem when the ship-generated waves could propagate upstream. A MEL method is therefore employed to investigate the upstream wave generated by the ship moving over the uneven bottom. The central differential scheme provides more accurate results, but it is not unconditionally stable. Simulation results show that the hydrodynamic interaction between the ship and the uneven bottom could initiate an upstream tsunami, as well as unsteady wave-making resistance on ships. The unsteady wave-making resistance oscillates periodically, and the amplitude and period of the oscillations are highly dependent on speed and water depth.
Original languageEnglish
Article number114073
Number of pages10
JournalOcean Engineering
Early online date14 Mar 2023
Publication statusE-pub ahead of print - 14 Mar 2023


  • uneven bottom
  • upstream wave
  • unsteady wave resistance
  • numerical simulation
  • periodic oscillation


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