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Polish Maritime Research

The Journal of Gdansk University of Technology

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Volume 23, Issue s1


Extended Elliptic Mild Slope Equation Incorporating the Nonlinear Shoaling Effect

Qian-lu Xiao
  • Corresponding author
  • Key Laboratory of Coastal Disaster and Defence, Ministry of Education, Hohai University, Nanjing, China China
  • College of Harbour, Coastal and Offshore Engineering, Hohai University, Nanjing, China
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Chun-hui Li
  • Key Laboratory of Coastal Disaster and Defence, Ministry of Education, Hohai University, Nanjing, China
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Xiao-yan Fu
  • Key Laboratory of Coastal Disaster and Defence, Ministry of Education, Hohai University, Nanjing, China
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Mei-ju Wang
  • Key Laboratory of Coastal Disaster and Defence, Ministry of Education, Hohai University, Nanjing, China
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2016-11-16 | DOI: https://doi.org/10.1515/pomr-2016-0045


The transformation during wave propagation is significantly important for the calculations of hydraulic and coastal engineering, as well as the sediment transport. The exact wave height deformation calculation on the coasts is essential to near-shore hydrodynamics research and the structure design of coastal engineering. According to the wave shoaling results gained from the elliptical cosine wave theory, the nonlinear wave dispersion relation is adopted to develop the expression of the corresponding nonlinear wave shoaling coefficient. Based on the extended elliptic mild slope equation, an efficient wave numerical model is presented in this paper for predicting wave deformation across the complex topography and the surf zone, incorporating the nonlinear wave dispersion relation, the nonlinear wave shoaling coefficient and other energy dissipation factors. Especially, the phenomenon of wave recovery and second breaking could be shown by the present model. The classical Berkhoff single elliptic topography wave tests, the sinusoidal varying topography experiment, and complex composite slopes wave flume experiments are applied to verify the accuracy of the calculation of wave heights. Compared with experimental data, good agreements are found upon single elliptical topography and one-dimensional beach profiles, including uniform slope and step-type profiles. The results indicate that the newly-developed nonlinear wave shoaling coefficient improves the calculated accuracy of wave transformation in the surf zone efficiently, and the wave breaking is the key factor affecting the wave characteristics and need to be considered in the nearshore wave simulations.

Keywords: nonlinear dispersion relation; nonlinear shoaling coefficient; extended elliptic mild slope equation; surf zone; wave transformation


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About the article

Published Online: 2016-11-16

Published in Print: 2016-10-01

Citation Information: Polish Maritime Research, Volume 23, Issue s1, Pages 44–51, ISSN (Online) 2083-7429, DOI: https://doi.org/10.1515/pomr-2016-0045.

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© 2016. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

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