Unsteady hydrodynamics of a surface piercing and fully submerged body when entering a lock

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Ship hydrodynamics in a constant waterway have been well studied. With a coordinate system fixed on the moving ship, the boundary value problem (BVP) is usually treated as a steady one. However, the hydrodynamics of a ship moving in confined waterways with abrupt changes in width or depth are complex due to their unsteady nature. The studies on such unsteady problems are insufficient. In the engineering practise, the hydrodynamic unsteadiness can be fully reflected by a scenario when a ship enters a lock. Prior studies have predominantly focused on predicting the ships’ hydrodynamic forces without considering the unsteady terms on the free-surface boundary conditions. Obviously, such steady or quasi-steady methods overlooked the crucial unsteady phenomenons on free water surface. To address this gap, the present study introduces a novel three-level difference scheme to discretize the free surface condition, preserving unsteady terms while maintaining temporal continuity of cells on the free surface. With the implementation of such fully unsteady BVP, we observed some interesting unsteady free surface motions which were not well documented in the existing literature. To verify our new observations, as well as to validate the numerical method proposed in this study, two physical model tests were designed and conducted in a towing tank: a submerged ellipsoid enters into a deep lock at relatively high speeds, and a box enters into a shallow and narrow lock at very low speeds. The discussions are highlighted on the unsteady waves in front of the moving bodies, as well as
the unsteady resistance induced by such waves.
Original languageEnglish
Article number063111
JournalPhysics of Fluids
Issue number6
Publication statusPublished - 25 Jun 2024


  • potential flow theory
  • hydrodynamics
  • unsteady effect
  • ship-lock problem


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