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 and W. C. Webster
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W. Y. Duan: Harbin Engineering University
K. Zheng: Harbin Engineering University
B. B. Zhao: Harbin Engineering University
Z. Demirbilek: Army Engineering Research and Design Center
R. C. Ertekin: University of Hawaii at Manoa
W. C. Webster: University of California

Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, 2016, vol. 84, issue 2, No 10, 567-583

Abstract: Abstract 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.

Keywords: Wave–current interaction; Green–Naghdi theory; Shallow water waves; Submerged bar (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s11069-016-2464-0

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