Abstract
Tsunamis are traveling waves which are characterized by long wavelengths and large amplitudes close to the shore. Due to the transformation of tsunamis, undular bores have been frequently observed in the coastal zone and can be viewed as a sequence of solitary waves with different wave heights and different separation distances among them. In this article, transient harbor oscillations induced by incident successive solitary waves are first investigated. The transient oscillations are simulated by a fully nonlinear Boussinesq model, FUNWAVE-TVD. The incident successive solitary waves include double solitary waves and triple solitary waves. This paper mainly focuses on the effects of different waveform parameters of the incident successive solitary waves on the relative wave energy distribution inside the harbor. These wave parameters include the incident wave height, the relative separation distance between adjacent crests, and the number of elementary solitary waves in the incident wave train. The relative separation distance between adjacent crests is defined as the ratio of the distance between adjacent crests in the incident wave train to the effective wavelength of the single solitary wave. Maximum oscillations inside the harbor excited by various incident waves are also discussed. For comparison, the transient oscillation excited by the single solitary wave is also considered. The harbor used in this paper is assumed to be long and narrow and has constant depth; the free surface movement inside the harbor is essentially one-dimensional. This study reveals that, for the given harbor and for the variation ranges of all the waveform parameters of the incident successive solitary waves studied in this paper, the larger incident wave heights and the smaller number of elementary solitary waves in the incident tsunami lead to a more uniform relative wave energy distribution inside the harbor. For the successive solitary waves, the larger relative separation distance between adjacent crests can cause more obvious fluctuations of the relative wave energy distribution over different resonant modes. When the wave height of the elementary solitary wave in the successive solitary waves equals to that of the single solitary wave and the relative separation distance between adjacent crests is equal to or greater than 0.6, the maximum oscillation inside the harbor induced by the successive solitary waves is almost identical to that excited by the single solitary wave.
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Acknowledgements
This work was financially supported by the National Natural Science Foundation of China (Grant nos. 51609108, 51309124 and 51679113), the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (Grant no. 16KJB570004), the State Key Laboratory of Coastal and Offshore Engineering at Dalian University of Technology (Grant no. LP1602), the Jiangsu Key Laboratory of Coast Ocean Resources Development and Environment Security at Hohai University (Grant no. JSCE201508), and the Jiangsu Key Laboratory of Advanced Design and Manufacturing Technology for Ship at Jiangsu University of Science and Technology (Grant no. CJ1504).
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Gao, J., Ji, C., Liu, Y. et al. Numerical study on transient harbor oscillations induced by successive solitary waves. Ocean Dynamics 68, 193–209 (2018). https://doi.org/10.1007/s10236-017-1121-9
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DOI: https://doi.org/10.1007/s10236-017-1121-9