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 William C. Webster,Wenyang Duan and Binbin Zhao.Green-Naghdi Theory, Part A: Green-Naghdi (GN) Equations for Shallow Water Waves[J].Journal of Marine Science and Application,2011,(3):253-258.[doi:10.1007/s11804-011-1066-1]
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Green-Naghdi Theory, Part A: Green-Naghdi (GN) Equations for Shallow Water Waves


Green-Naghdi Theory, Part A: Green-Naghdi (GN) Equations for Shallow Water Waves
William C. Webster Wenyang Duan and Binbin Zhao
William C. Webster Wenyang Duan and Binbin Zhao
1. Department of Civil & Environmental Engineering, University of California, Berkeley CA 94720-1710, USA 2. College of Shipbuilding Engineering, Harbin Engineering University, 150001 Harbin, China
Green-Naghdi (GN) equations dispersion relation wave-absorbing beach shallow-water waves
In this work, Green-Naghdi (GN) equations with general weight functions were derived in a simple way. A wave-absorbing beach was also considered in the general GN equations. A numerical solution for a level higher than 4 was not feasible in the past with the original GN equations. The GN equations for shallow water waves were simplified here, which make the application of high level (higher than 4) equations feasible. The linear dispersion relationships of the first seven levels were presented. The accuracy of dispersion relationships increased as the level increased. Level 7 GN equations are capable of simulating waves out to wave number times depth . Numerical simulation of nonlinear water waves was performed by use of Level 5 and 7 GN equations, which will be presented in the next paper.


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Supported by the Special Fund for Basic Scientific Research of Central Colleges, Harbin Engineering University (Harbin), the National Natural Science Foundation of China, Doctor Subject Foundation of the Ministry of Education of China, and the “111” project (B07019)
Last Update: 2011-09-13