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Open AccessFeature PaperArticle

Simulation of Ocean Circulation of Dongsha Water Using Non-Hydrostatic Shallow-Water Model

1
Department of Marine Environmental Informatics, National Taiwan Ocean University, Keelung 20224, Taiwan
2
Center of Excellence for Ocean Engineering, National Taiwan Ocean University, Keelung 20224, Taiwan
3
CECI Engineering Consultants, Inc., Taipei 11491, Taiwan
4
Department of Civil and Water Resources Engineering, National Chiayi University, Chiayi 60004, Taiwan
5
Department of Harbor & River Engineering, National Taiwan Ocean University, Keelung 20224, Taiwan
*
Authors to whom correspondence should be addressed.
Water 2020, 12(10), 2832; https://doi.org/10.3390/w12102832
Received: 7 September 2020 / Revised: 5 October 2020 / Accepted: 6 October 2020 / Published: 12 October 2020
(This article belongs to the Special Issue Wave and Tide Modelling in Coastal and Ocean Hydrodynamics)
A two-dimensional non-hydrostatic shallow-water model for weakly dispersive waves is developed using the least-squares finite-element method. The model is based on the depth-averaged, nonlinear and non-hydrostatic shallow-water equations. The non-hydrostatic shallow-water equations are solved with the semi-implicit (predictor-corrector) method and least-squares finite-element method. In the predictor step, hydrostatic pressure at the previous step is used as an initial guess and an intermediate velocity field is calculated. In the corrector step, a Poisson equation for the non-hydrostatic pressure is solved and the final velocity and free-surface elevation is corrected for the new time step. The non-hydrostatic shallow-water model is verified and applied to both wave and flow driven fluid flows, including solitary wave propagation in a channel, progressive sinusoidal waves propagation over a submerged bar, von Karmann vortex street, and ocean circulations of Dongsha Atolls. It is found hydrostatic shallow-water model is efficient and accurate for shallow water flows. Non-hydrostatic shallow-water model requires 1.5 to 3.0 more cpu time than hydrostatic shallow-water model for the same simulation. Model simulations reveal that non-hydrostatic pressure gradients could affect the velocity field and free-surface significantly in case where nonlinearity and dispersion are important during the course of wave propagation. View Full-Text
Keywords: hydrostatic; non-hydrostatic; ocean circulation; shallow-water equations; solitary wave; von Karmann vortex street; weakly dispersive hydrostatic; non-hydrostatic; ocean circulation; shallow-water equations; solitary wave; von Karmann vortex street; weakly dispersive
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MDPI and ACS Style

Liang, S.-J.; Young, C.-C.; Dai, C.; Wu, N.-J.; Hsu, T.-W. Simulation of Ocean Circulation of Dongsha Water Using Non-Hydrostatic Shallow-Water Model. Water 2020, 12, 2832.

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