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Accuracy of depth-integrated nonhydrostatic wave models

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journal contribution
posted on 2019-01-14, 12:04 authored by Gang Wang, Jinhai Zheng, Qiuhua LiangQiuhua Liang
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.

Funding

This research was supported by the National Key Research and Development Program of China (No.: 2017YFC1404205), the National Natural Science Foundation of China (NO.: 51579090) and the Fundamental Research Funds for the Central Universities (NO.: 2015B15714).

History

School

  • Architecture, Building and Civil Engineering

Published in

Ocean Engineering

Volume

149

Pages

217 - 225

Citation

WANG, G., ZHENG, J. and LIANG, Q., 2018. Accuracy of depth-integrated nonhydrostatic wave models. Ocean Engineering, 149, pp.217-225.

Publisher

© Elsevier

Version

  • AM (Accepted Manuscript)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Acceptance date

2017-12-06

Publication date

2017-12-27

Notes

This paper was published in the journal Ocean Engineering and the definitive published version is available at https://doi.org/10.1016/j.oceaneng.2017.12.015.

ISSN

0029-8018

Language

  • en