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Run-up of non-breaking double solitary waves with equal wave heights on a plane beach

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Abstract

The evolution and run-up of double solitary waves on a plane beach were studied numerically using the nonlinear shallow water equations (NSWEs) and the Godunov scheme. The numerical model was validated through comparing the present numerical results with analytical solutions and laboratory measurements available for propagation and run-up of single solitary wave. Two successive solitary waves with equal wave heights and variable separation distance of two crests were used as the incoming wave on the open boundary at the toe of a slope beach. The run-ups of the first wave and the second wave with different separation distances were investigated. It is found that the run-up of the first wave does not change with the separation distance and the run-up of the second wave is affected slightly by the separation distance when the separation distance is gradually shortening. The ratio of the maximum run-up of the second wave to one of the first wave is related to the separation distance as well as wave height and slope. The run-ups of double solitary waves were compared with the linearly superposed results of two individual solitary-wave run-ups. The comparison reveals that linear superposition gives reasonable prediction when the separation distance is large, but it may overestimate the actual run-up when two waves are close.

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Authors and Affiliations

  1. School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China

    Dong Jie  (董杰)

  2. School of Naval Architecture, Ocean and Civil Engineering, MOE Key Laboratory of Hydrodynamics, Shanghai Jiao Tong University, Shanghai, 200240, China

    Wang Ben-long  (王本龙) & Liu Hua  (刘桦)

Authors
  1. Dong Jie  (董杰)
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  2. Wang Ben-long  (王本龙)
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  3. Liu Hua  (刘桦)
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Corresponding author

Correspondence to Liu Hua  (刘桦).

Additional information

Project supported by the National Natural Science Foundation of China (Grant No. 51379123), the Natural Science Foundation of Shanghai Municipality (Grant No. 11ZR1418200) and the Shanghai Water Authority and the State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University (Grant No. GKZD010063).

Biography: DONG Jie (1988-), Male, Ph. D. Candidate

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Dong, J., Wang, Bl. & Liu, H. Run-up of non-breaking double solitary waves with equal wave heights on a plane beach. J Hydrodyn 26, 939–950 (2014). https://doi.org/10.1016/S1001-6058(14)60103-7

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  • DOI: https://doi.org/10.1016/S1001-6058(14)60103-7

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