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Statistical Analyses of Wave Height Distribution for Multidirectional Irregular Waves over A Sloping Bottom

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Abstract

The main objective of this paper is to examine the influences of both the principal wave direction and the directional spreading parameter of the wave energy on the wave height evolution of multidirectional irregular waves over an impermeable sloping bottom and to propose an improved wave height distribution model based on an existing classical formula. The numerical model FUNWAVE 2.0, based on a fully nonlinear Boussinesq equation, is employed to simulate the propagation of multidirectional irregular waves over the sloping bottom. Comparisons of wave heights derived from wave trains with various principal wave directions and different directional spreading parameters are conducted. Results show that both the principal wave direction and the wave directional spread have significant influences on the wave height evolution on a varying coastal topography. The shoaling effect for the wave height is obviously weakened with the increase of the principal wave direction and with the decrease of the directional spreading parameter. With the simulated data, the classical Klopman wave height distribution model is improved by considering the influences of both factors. It is found that the improved model performs better in describing the wave height distribution for the multidirectional irregular waves in shallow water.

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References

  • Battjes, J.A. and Groenendijk, H.W., 2000. Wave height distributions on shallow foreshores, Coastal Engineering, 40(3), 161–182.

    Article  Google Scholar 

  • Bouws, E., Günther, H., Rosenthal, W. and Vincent, C., 1985. Similarity of the wind wave spectrum in finite depth water: 1. Spectral form, Journal of Geophysical Research, 90(C1), 975–986.

    Article  Google Scholar 

  • Chawla, A. and Kirby, J.T., 2000. A source function method for generation of waves on currents in Boussinesq models, Applied Ocean Research, 22, 75–83.

    Article  Google Scholar 

  • Chen, H.Z., Jiang, D.H., Tang, X.C. and Mao, H.F., 2019. Evolution of irregular wave shape over a fringing reef flat, Ocean Engineering, 192, 106544.

    Article  Google Scholar 

  • Donelan, M.A., 2001. A new method for directional wave analysis based on wavelets, Proceedings of the 4th International Symposium on Ocean Wave Measurement and Analysis, American Society of Civil Engineers, San Francisco, pp. 310–317.

    Google Scholar 

  • Forristall, G.Z., 1978. On the statistical distribution of wave heights in a storm, Journal of Geophysical Research, 83(C5), 2353–2358.

    Article  Google Scholar 

  • Gallagher, E.L., Elgar, S. and Guza, R.T., 1998. Observations of sand bar evolution on a natural beach, Journal of Geophysical Research, 103(C2), 3203–3215.

    Article  Google Scholar 

  • Gao, J.L., Ji, C.Y., Liu, Y.Y., Ma, X.J. and Gaidai, O., 2017. Influence of offshore topography on the amplification of infragravity oscillations within a harbor, Applied Ocean Research, 65, 129–141.

    Article  Google Scholar 

  • Gao, J.L., Ma, X.Z., Dong, G.H., Chen, H.Z., Liu, Q. and Zang, J., 2021. Investigation on the effects of Bragg reflection on harbor oscillations, Coastal Engineering, 103977. doi: https://doi.org/10.1016/j.coastaleng.2021.103977.

  • Gao, J.L., Ma, X.Z., Zang, J., Dong, G.H., Ma, X.J., Zhu, Y.Z. and Zhou, L., 2020. Numerical investigation of harbor oscillations induced by focused transient wave groups, Coastal Engineering, 158, 103670.

    Article  Google Scholar 

  • Gao, J.L., Zhou, X.J., Zang, J., Chen, Q. and Zhou, L., 2018. Influence of offshore fringing reefs on infragravity period oscillations within a harbor, Ocean Engineering, 158, 286–298.

    Article  Google Scholar 

  • Gao, J.L., Zhou, X.J., Zhou, L., Zang, J. and Chen, H.Z., 2019. Numerical investigation on effects of fringing reefs on low-frequency oscillations within a harbor, Ocean Engineering, 172, 86–95.

    Article  Google Scholar 

  • Glukhovskii, B.K., 1966. Investigation of Sea Wind Waves, Gidrometeoizdat Publisher. (in Russian).

  • Goda, Y., 1999. A comparative review on the functional forms of directional wave spectrum, Coastal Engineering Journal, 41(1), 1–20.

    Article  Google Scholar 

  • Goda, Y., 2010. Random Seas and Design of Maritime Structures, third ed., World Scientific, Hackensack.

    Book  Google Scholar 

  • Hsu, T.W., Hsu, J.R.C., Weng, W.K., Wang, S.K. and Ou, S.H., 2006. Wave setup and setdown generated by obliquely incident waves, Coastal Engineering, 53(10), 865–877.

    Article  Google Scholar 

  • Hur, D.S., 2004. Deformation of multi-directional random waves passing over an impermeable submerged breakwater installed on a sloping bed, Ocean Engineering, 31(10), 1295–1311.

    Article  Google Scholar 

  • Hur, D.S., Kawashima, N. and Iwata, K., 2003. Experimental study of the breaking limit of multi-directional random waves passing over an impermeable submerged breakwater, Ocean Engineering, 30(15), 1923–1940.

    Article  Google Scholar 

  • Ilic, S., van der Westhuysen, A. J., Roelvink, J.A. and Chadwick, A.J., 2007. Multidirectional wave transformation around detached breakwaters, Coastal Engineering, 54(10), 775–789.

    Article  Google Scholar 

  • Ji, X.R., Liu, S.X., Li, J.X. and Jia, W., 2015. Experimental investigation of the interaction of multidirectional irregular waves with a large cylinder, Ocean Engineering, 93, 64–73.

    Article  Google Scholar 

  • Karmpadakis, I., Swan, C. and Christou, M., 2020. Assessment of wave height distributions using an extensive field database, Coastal Engineering, 157, 103630.

    Article  Google Scholar 

  • Katsardi, V., de Lutio, L. and Swan, C., 2013. An experimental study of large waves in intermediate and shallow water depths. Part I: wave height and crest height statistics, Coastal Engineering, 73, 43–57.

    Article  Google Scholar 

  • Kirby, J.T., Long, W. and Shi, F., 2003. Funwave 2.0 Fully Nonlinear Boussinesq Wave Model on Curvilinear Coordinates, University of Delaware, Newark.

    Google Scholar 

  • Klopman, G. and Stive, M.J.F., 1989. Extreme waves and wave loading in shallow water, Proceedings of Wave and Current Kinematics and Loading: E&P Forum Workshop, Paris, France.

  • Klopman, G., 1996. Extreme Wave Heights in Shallow Water, Delft Hydraulics. The Netherlands.

    Google Scholar 

  • Li, J.X., Wang, Z.H. and Liu, S.X., 2014. Experimental study of interactions between multi-directional focused wave and vertical circular cylinder, part II: wave force, Coastal Engineering, 83, 233–242.

    Article  Google Scholar 

  • Li, Y.S., Liu, S.X., Yu, Y.X. and Lai, G.Z., 2000. Numerical modelling of multi-directional irregular waves through breakwaters, Applied Mathematical Modelling, 24(8–9), 551–574.

    Article  Google Scholar 

  • Liu, S.X., Sun, Z.B. and Li, J.X., 2012. An unstructured FEM model based on Boussinesq equations and its application to the calculation of multidirectional wave run-up in a cylinder group, Applied Mathematical Modelling, 36(9), 4146–4164.

    Article  MathSciNet  Google Scholar 

  • Liu, Y., Li, S.W., Chen, S.G., Hu, C.Y., Fan, Z.F. and Jin, R.J., 2020a. Random wave overtopping of vertical seawalls on coral reefs, Applied Ocean Research, 100, 102166.

    Article  Google Scholar 

  • Liu, Y., Li, S.W., Zhao, X., Hu, C.Y., Fan, Z.F. and Chen, S.G., 2020b. Artificial neural network prediction of overtopping rate for impermeable vertical seawalls on coral reefs, Journal of Waterway, Port, Coastal, and Ocean Engineering, 146(4), 04020015.

    Article  Google Scholar 

  • Liu, W.J., Shao, K.Q., Ning, Y. and Zhao, X.Z., 2020. Numerical study of the impact of climate change on irregular wave run-up over reef-fringed coasts, China Ocean Engineering, 34(2), 162–171.

    Article  Google Scholar 

  • Longuet-Higgins, M.S., 1952. On the statistical distribution of the heights of sea waves, Journal of Marine Research, 11(5), 245–266.

    Google Scholar 

  • Longuet-Higgins, M.S., Cartwright, D.E. and Smith, N.D., 1963. Observations of the directional spectrum of sea waves using the motions of a floating buoy, in: Ocean Wave Spectra, Englewood Cliffs, New York, pp. 111–136.

  • Ma, Y.X., Chen, H.Z., Ma, X.Z. and Dong, G.H., 2017. A numerical investigation on nonlinear transformation of obliquely incident random waves on plane sloping bottoms, Coastal Engineering, 130, 65–84.

    Article  Google Scholar 

  • Mendez, F.J., Losada, I.J. and Medina, R., 2004. Transformation model of wave height distribution on planar beaches, Coastal Engineering, 50(3), 97–115.

    Article  Google Scholar 

  • Naess, A., 1985. On the distribution of crest to trough wave heights, Ocean Engineering, 12(3), 221–234.

    Article  Google Scholar 

  • Orimoloye, S., Karunarathna, H. and Reeve, D.E., 2019. Effects of swell on wave height distribution of energy-conserved bimodal seas, Journal of Marine Science and Engineering, 7(3), 79.

    Article  Google Scholar 

  • Shi, F.Y., Dalrymple, R.A., Kirby, J.T., Chen, Q. and Kennedy, A., 2001. A fully nonlinear Boussinesq model in generalized curvilinear coordinates, Coastal Engineering, 42(4), 337–358.

    Article  Google Scholar 

  • Stansell, P., 2005. Distributions of extreme wave, crest and trough heights measured in the North Sea, Ocean Engineering, 32(8–9), 1015–1036.

    Article  Google Scholar 

  • van Vledder, G., 1991. Modification of the Glukhovskiy Distribution, Delft Hydraulics.

  • Vincent, C.L. and Briggs, M.J., 1989. Refraction—diffraction of irregular waves over a mound, Journal of Waterway, Port, Coastal, and Ocean Engineering, 115(2), 269–284.

    Article  Google Scholar 

  • Wei, G., Kirby, J.T., Grilli, S.T. and Subramanya, R., 1995. A fully nonlinear Boussinesq model for surface waves. Part 1. Highly nonlinear unsteady waves, Journal of Fluid Mechanics, 294, 71–92.

    Article  MathSciNet  Google Scholar 

  • Yang, Z.W., Liu, S.X., Ji, X.R., Bingham, H.B., Zhang, H.Q. and Xie, M.X., 2021a. A generalized second-order 3D theory for coupling multidirectional wave propagation from a numerical model to a physical model. Part I: Derivation, implementation and model verification, Coastal Engineering, 165, 103864.

    Article  Google Scholar 

  • Yang, Z.W., Liu, S.X., Ji, X.R., Bingham, H.B., Zhang, H.Q. and Xie, M.X., 2021b. A generalized second-order 3D theory for coupling multidirectional wave propagation from a numerical model to a physical model. Part II: Experimental validation using an I-shaped segmented wavemaker, Coastal Engineering, 165, 103863.

    Article  Google Scholar 

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Authors and Affiliations

  1. School of Naval Architecture and Ocean Engineering, Jiangsu University of Science and Technology, Zhenjiang, 212100, China

    Jun-liang Gao, Zhen Liu & Qian Liu

  2. School of Marine Engineering Equipment, Zhejiang Ocean University, Zhoushan, 316022, China

    Hong-zhou Chen

  3. Henan Province Construction Engineering Quality Inspection and Testing Center Station Co. Ltd., Zhengzhou, 450053, China

    Li-li Mei

  4. State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian, 116024, China

    Hong-zhou Chen & Li-li Mei

Authors
  1. Jun-liang Gao
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  2. Hong-zhou Chen
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  3. Li-li Mei
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  4. Zhen Liu
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  5. Qian Liu
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Correspondence to Hong-zhou Chen.

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This research is financially supported by the National Natural Science Foundation of China (Grant No. 51809039), the Natural Science Foundation of Jiangsu Province (Grant No. BK20201455), the Natural Science Foundation of the Jiangsu Higher Education Institutions (Grant No. 20KJD170005) and the Qing Lan Project of Jiangsu Universities.

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Gao, Jl., Chen, Hz., Mei, Ll. et al. Statistical Analyses of Wave Height Distribution for Multidirectional Irregular Waves over A Sloping Bottom. China Ocean Eng 35, 504–517 (2021). https://doi.org/10.1007/s13344-021-0046-8

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  • DOI: https://doi.org/10.1007/s13344-021-0046-8

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