|Table of Contents|

Citation:
　Shiliang Duan,Binbin Zhao,and W. C. Webster.Green–Naghdi Theory, Part B: Green–Naghdi Equations for Deep Water Waves[J].Journal of Marine Science and Application,2023,(1):44-51.[doi:10.1007/s11804-023-00316-y]
Click and Copy

Green–Naghdi Theory, Part B: Green–Naghdi Equations for Deep Water Waves

Info

Title:
Green–Naghdi Theory, Part B: Green–Naghdi Equations for Deep Water Waves
Author(s):
Shiliang Duan1;  Binbin Zhao1;  and W. C. Webster2
Affilations:
Author(s):
Shiliang Duan1;  Binbin Zhao1;  and W. C. Webster2
1 College of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, China;
2 Civil & Environmental Engineering, University of California, Berkeley CA94704, USA
Keywords:
Green–Naghdi equations|Finite difference|Water waves|Deep water|Focused waves
分类号:
-
DOI:
10.1007/s11804-023-00316-y
Abstract:
“Green–Naghdi Theory, Part A: Green–Naghdi (GN) Equations for Shallow Water Waves” have investigated the linear dispersion relations of high-level GN equations in shallow water. In this study, the GN equations for deep water waves are investigated. In the traditional GN equations for deep water waves, the velocity distribution assumption involves only one representative wave number. Herein, a new velocity distribution shape function with multiple representative wave numbers is employed. Further, we have derived the three-dimensional GN equations and analyzed the linear dispersion relations of the GN-3 and GN-5 equations. In this study, the finite difference method is used to simulate focus waves in the time domain. Additionally, the GN-5 equations are used to validate the wave profile and horizontal velocity distribution along water depth for different focused waves.

References:

Baldock TE, Swan C, Taylor PH (1996) A laboratory study of nonlinear surface waves on water. Philosophical Transactions of the Royal Society of London. Series A:Mathematical, Physical and Engineering Sciences 354(1707):649-676. DOI:10.1098/rsta.1996.0022
Demirbilek Z, Webster WC (1992) Application of the Green-Naghdi theory of fluid sheets to shallow-water wave problems. Report 1.Model Development. Coastal Engineering Research Center, Vicksburg, Technical Report No. CERC-92-11. https://doi.org/10.1017/S0022112086000630
Ertekin RC, Webster WC, Wehausen JV (1986) Waves caused by a moving disturbance in a shallow channel of finite width. J Fluid Mech 169:275-292. https://doi.org/10.1017/S0022112086000630
Green AE, Laws N, Naghdi PM (1974) On the theory of water waves. Proc R Soc Lond A Math Phys Sci 338:43-55. https://doi.org/10.1098/rspa.1974.0072
Green AE, Naghdi PM (1976) Directed fluid sheets. Proc R Soc Lond A Math Phys Sci 347:447-473. https://doi.org/10.1098/rspa.1976.0011
Hayatdavoodi M, Treichel K, Ertekin RC (2019) Parametric study of nonlinear wave loads on submerged decks in shallow water. Journal of Fluids and Structures 86:266-289. https://doi.org/10.1016/j.jfluidstructs.2019.02.016
Hayatdavoodi M, Liu J, Ertekin RC (2022) Bore impact on decks of coastal structures. Journal of Waterway, Port, Coastal, and Ocean Engineering 148(2):04021051. DOI:10.1061/(ASCE)WW.1943-5460.0000696
Hayatdavoodi M, Ertekin RC (2022) On some nonlinear wave diffraction and refraction solutions in shallow waters. International Conference on Offshore Mechanics and Arctic Engineering, Vol. 85895, V05AT06A004
Kostikov VK, Hayatdavoodi M, Ertekin RC (2022) Drift of elastic floating ice sheets by waves and current:Multiple sheets. Physics of Fluids 34(5):057113. DOI:10.1063/5.0091538
Liu J, Hayatdavoodi M, Ertekin RC (2019) Bore pressure on horizontal and vertical surfaces. International Conference on Offshore Mechanics and Arctic Engineering, Vol. 58844, V07AT06A008. DOI:10.1115/OMAE2019-96013
Liu J, Hayatdavoodi M, Ertekin RC (2020) On bore dynamics and pressure:RANS, Green-Naghdi, and Saint-Venant equations. Journal of Offshore Mechanics and Arctic Engineering 142(2):021902. DOI:10.1115/1.4044988
Wang Z, Zhao BB, Duan WY, Ertekin RC, Hayatdavoodi M, Zhang TY (2020) On solitary wave in nonuniform shear currents.Journal of Hydrodynamics 32(4):800-805. DOI:10.1007/s42241-020-0051-z
Webster WC, Kim DY (1991) The dispersion of large-amplitude gravity waves in deep water. Water Waves, 397-416. https://trid.trb.org/view/439579
Webster WC, Duan WY, Zhao BB (2011) Green-Naghdi theory, part A:Green-Naghdi (GN) equations for shallow water waves.Journal of Marine Science and Application 10(3):253-258. DOI:10.1007/s11804-011-1066-1
Webster WC, Zhao BB (2018) The development of a high-accuracy, broadband, Green-Naghdi model for steep, deep-water ocean waves. Journal of Ocean Engineering and Marine Energy 4(4):273-291. DOI:10.1007/s40722-018-0122-1
Zhao BB, Duan WY, Ertekin RC (2014) Application of higher-level GN theory to some wave transformation problems. Coastal Engineering 83:177-189. DOI:10.1016/j.coastaleng.2013.10.010
Zhao BB, Zheng K, Duan WY, Ertekin RC, Shao YL (2020) Time domain simulation of focused waves by High-Level Irrotational Green-Naghdi equations and Harmonic Polynomial Cell method.European Journal of Mechanics-B/Fluids 82:83-92. DOI:10.1016/j.euromechflu.2020.02.006
Zheng K, Zhao BB, Duan WY, Ertekin RC, Chen XB (2016) Simulation of evolution of gravity wave groups with moderate steepness. Ocean Modelling 98:1-11. DOI:10.1016/j.ocemod. 2015.12.003

Memo

Memo:
Received date:2022-12-3;Accepted date:2022-12-12。<br>Corresponding author:Zhao Binbin,E-mail:zhaobinbin@hrbeu.edu.cn
Last Update: 2023-04-10