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Accuracy of depth-integrated nonhydrostatic wave models

Lookup NU author(s): Dr Gang Wang, Professor Qiuhua Liang



This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND).


© 2017 Elsevier Ltd Depth-integrated nonhydrostatic models have been wildly used to simulate propagation of waves. Yet, there lacks a well-documented theoretical framework that can be used to assess the accuracy and scope of applications of these models and the related numerical approaches. In this work, we carry out Stokes-type Fourier and shoaling analyses to examine the linear and nonlinear properties of a popular one-layer depth-integrated nonhydrostatic model derived by Stelling and Zijlema (2003). The theoretical analysis shows that the model can satisfactorily interpret the dispersity for linear waves but presents evident divergence for nonlinear solutions even when kd → 0. A generalized depth-integrated nonhydrostatic formulation using arbitrary elevation as a variable is then derived and analyzed to examine the effects of neglecting advective and diffusive nonlinear terms in the previous studies and explore possible improvements in numerical solutions for wave propagation. Compared with the previous studies, the new generalized formulation exhibits similar dispersion relationship and improved shoaling effect. However, no significant improvement is presented for the nonlinear properties, indicating that retaining neglected nonlinear terms may not significantly improve the nonlinear performance of the nonhydrostatic model. Further analysis shows that the nonlinear properties of the depth-integrated nonhydrostatic formulation may be improved by defining variables at one-third of the still water level. However, such an improvement comes at the price of decreasing accuracy in describing dispersion and shoaling properties.

Publication metadata

Author(s): Wang G, Zheng J, Liang Q

Publication type: Article

Publication status: Published

Journal: Ocean Engineering

Year: 2018

Volume: 149

Pages: 217-225

Print publication date: 01/02/2018

Online publication date: 27/12/2017

Acceptance date: 06/12/2017

Date deposited: 06/03/2018

ISSN (print): 0029-8018

ISSN (electronic): 1873-5258

Publisher: Elsevier Ltd


DOI: 10.1016/j.oceaneng.2017.12.015


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