Natural Hazards

, Volume 84, Supplement 2, pp 567–583 | Cite as

On wave–current interaction by the Green–Naghdi equations in shallow water

  • W. Y. Duan
  • K. Zheng
  • B. B. Zhao
  • Z. Demirbilek
  • R. C. Ertekin
  • W. C. Webster
Original Paper


This work is on the use of the Green–Naghdi (GN) nonlinear wave equations for simulating wave–current interaction in shallow water. The stream-function wave theory is used at the wave-maker boundary to generate nonlinear incident waves to consider the wave–current interaction. The nonlinear GN equations are solved in the time domain by use of the finite-difference method. The model is evaluated with data from three experimental studies. A strong opposing current over a submerged bar is investigated in the first test case. In the second test case, the interaction of waves with a uniform current over flat bottom is considered. In the third case, wave–current interaction over a variable bathymetry with the following and opposing currents is studied. The numerical results obtained by the GN equations are compared with the experimental data and results based on the Boussinesq equations. A good agreement is obtained for the three experimental studies considered for a wide range of wave and current conditions.


Wave–current interaction Green–Naghdi theory Shallow water waves Submerged bar 



The first and third authors’ (W.Y. Duan and B.B. Zhao) work is supported by the National Natural Science Foundation of China (Nos. 51490671, 11572093), International Science and Technology of Cooperation Project sponsored by Nation Ministry of Science and Technology of China (No. 2012DFA70420), the special Fund for Basic Scientific Research of Central Colleges (Harbin Engineering University) and High-Tech Ship Research Projects Sponsored by the Ministry of Industry and Information Technology (MIIT) of China.


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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  • W. Y. Duan
    • 1
  • K. Zheng
    • 1
  • B. B. Zhao
    • 1
  • Z. Demirbilek
    • 2
  • R. C. Ertekin
    • 3
  • W. C. Webster
    • 4
  1. 1.College of Shipbuilding EngineeringHarbin Engineering UniversityHarbinChina
  2. 2.Coastal Hydraulics LaboratoryArmy Engineering Research and Design CenterVicksburgUSA
  3. 3.Department of Ocean and Resources EngineeringUniversity of Hawaii at ManoaHonoluluUSA
  4. 4.Department of Civil and Environmental EngineeringUniversity of CaliforniaBerkeleyUSA

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