A numerical model for simulation of near-shore waves and wave induced currents using the depth-averaged non-hydrostatic shallow water equations with an improvement of wave energy dissipation

Phung Dang Hieu, Phan Ngoc Vinh


This study proposes a numerical model based on the depth-integrated non-hydrostatic shallow water equations with an improvement of wave breaking dissipation. Firstly, studies of parameter sensitivity were carried out using the proposed numerical model for simulation of wave breaking to understand the effects of the parameters of the breaking model on wave height distribution. The simulated results of wave height near the breaking point were very sensitive to the time duration parameter of wave breaking. The best value of the onset breaking parameter is around 0.3 for the non-hydrostatic shallow water model in the simulation of wave breaking. The numerical results agreed well with the published experimental data, which confirmed the applicability of the present model to the simulation of waves in near-shore areas.


Waves in surf zone, non-hydrostatic shallow water model, wave breaking dissipation.

Full Text:



Deigaard, R., 1989. Mathematical modelling of waves in the surf zone. Prog. Rep, 69, 47–59.

Schäffer, H. A., Madsen, P. A., and Deigaard, R., 1993. A Boussinesq model for waves breaking in shallow water. Coastal Engineering, 20(3–4), 185–202.

Madsen, P. A., Sørensen, O. R., and Schäffer, H. A., 1997. Surf zone dynamics simulated by a Boussinesq type model. Part I. Model description and cross-shore motion of regular waves. Coastal Engineering, 32(4), 255–287.

Madsen, P. A., Sørensen, O. R., and Schäffer, H. A., 1997. Surf zone dynamics simulated by a Boussinesq type model. Part II: Surf beat and swash oscillations for wave groups and irregular waves. Coastal Engineering, 32(4), 289–319.

Zelt, J. A., 1991. The run-up of nonbreaking and breaking solitary waves. Coastal Engineering, 15(3), 205–246.

Kennedy, A. B., Chen, Q., Kirby, J. T., and Dalrymple, R. A., 2000. Boussinesq modeling of wave transformation, breaking, and runup. I: 1D. Journal of Waterway, Port, Coastal, and Ocean Engineering, 126(1), 39–47.

Chen, Q., Dalrymple, R. A., Kirby, J. T., Kennedy, A. B., and Haller, M. C., 1999. Boussinesq modeling of a rip current system. Journal of Geophysical Research: Oceans, 104(C9), 20617–20637.

Fang, K., and Liu, Z., 1999. Modeling Breaking Waves and Wave-induced Currents with Fully Nonlinear Boussinesq Equations. WSEAS Transactions on Fluid Mechanics, 9, 131–143.

Stelling, G., and Zijlema, M., 2003. An accurate and efficient finite‐difference algorithm for non‐hydrostatic free‐surface flow with application to wave propagation. International Journal for Numerical Methods in Fluids, 43(1), 1–23.

Walters, R. A., 2005. A semi‐implicit finite element model for non‐hydrostatic (dispersive) surface waves. International Journal for Numerical Methods in Fluids, 49(7), 721–737.

Zijlema, M., and Stelling, G. S., 2008. Efficient computation of surf zone waves using the nonlinear shallow water equations with non-hydrostatic pressure. Coastal Engineering, 55(10), 780–790.

Yamazaki, Y., Kowalik, Z., and Cheung, K. F., 2009. Depth‐integrated, non‐hydrostatic model for wave breaking and run‐up. International Journal for Numerical Methods in Fluids, 61(5), 473–497.

Smit, P., Zijlema, M., and Stelling, G., 2013. Depth-induced wave breaking in a non-hydrostatic, near-shore wave model. Coastal Engineering, 76, 1–16.

Wei, Z., and Jia, Y., 2014. Simulation of nearshore wave processes by a depth-integrated non-hydrostatic finite element model. Coastal engineering, 83, 93–107.

Lu, X., and Xie, S., 2016. Depth-averaged non-hydrostatic numerical modeling of nearshore wave propagations based on the FORCE scheme. Coastal Engineering, 114, 208–219.

Ting, F. C., and Kirby, J. T., 1994. Observation of undertow and turbulence in a laboratory surf zone. Coastal Engineering, 24(1–2), 51–80.

Kowalik, Z., Knight, W., Logan, T., and Whitmore, P., 2005. Numerical modeling of the global tsunami: Indonesian tsunami of 26 December 2004. Science of Tsunami Hazards, 23(1), 40–56.

Wei, G., Kirby, J. T., and Sinha, A., 1999. Generation of waves in Boussinesq models using a source function method. Coastal Engineering, 36(4), 271–299.

Hamm, L., 1993. Directional nearshore wave propagation over a rip channel: an experiment. In Coastal Engineering 1992 (pp. 226–239).

DOI: https://doi.org/10.15625/1859-3097/20/2/15087 Display counter: Abstract : 172 views. PDF : 26 views.

Editorial Office:

Vietnam Journal of Marine Science and Technology

1st Floor, A16 Building, 18 Hoang Quoc Viet Street, Cau Giay District, Hanoi, Vietnam

Tel: (+84) 024 3791 7411

E-mail: jmst@vjs.ac.vn