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.
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Article Highlights
• To derive three-dimensional deep water GN equations using a new velocity assumption for future short-crest wave simulation.
• To apply the new deep water GN equations to water wave simulation in the time domain for the first time.
• To give the linear solution of new deep water GN equations.
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Duan, S., Zhao, B. & Webster, W.C. Green-Naghdi Theory, Part B: Green-Naghdi Equations for Deep Water Waves. J. Marine. Sci. Appl. 22, 44–51 (2023). https://doi.org/10.1007/s11804-023-00316-y
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DOI: https://doi.org/10.1007/s11804-023-00316-y