Abstract
Green-Naghdi (G-N) theory is a fully nonlinear theory for water waves. Some researchers call it a fully nonlinear Boussinesq model. Different degrees of complexity of G-N theory are distinguished by “levels” where the higher the level, the more complicated and presumably more accurate the theory is. In the research presented here a comparison was made between two different levels of G-N theory, specifically level II and level III G-N restricted theories. A linear analytical solution for level III G-N restricted theory was given. Waves on a planar beach and shoaling waves were both simulated with these two G-N theories. It was shown for the first time that level III G-N restricted theory can also be used to predict fluid velocity in shallow water. A level III G-N restricted theory is recommended instead of a level II G-N restricted theory when simulating fully nonlinear shallow water waves.
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Foundation item: Supported by the National Natural Science Foundation of China under Grant No. 50779008 and the 111 Project (B07019).
Bin-bin Zhao was born in 1984. He is presently a PhD candidate for fluid mechanics at Harbin Engineering University. His current research interests include Green-Naghdi theory and nonlinear wave-body interactions based on BEM.
Wen-yang Duan was born in 1967. He is a professor and a PhD supervisor at Harbin Engineering University. His current research interests include nonlinear wave-body interactions, SPH method and Boussinesq model.
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Zhao, Bb., Duan, Wy. Fully nonlinear shallow water waves simulation using Green-Naghdi theory. J. Marine. Sci. Appl. 9, 1–7 (2010). https://doi.org/10.1007/s11804-010-9031-y
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DOI: https://doi.org/10.1007/s11804-010-9031-y