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Spatial energy evolution of focused waves generated in numerical wave tank

Xu, G., Zhou, Y., Yan, S. ORCID: 0000-0001-8968-6616 & Yuan, S. (2024). Spatial energy evolution of focused waves generated in numerical wave tank. Applied Ocean Research, 148, article number 104015. doi: 10.1016/j.apor.2024.104015


This paper numerically investigates the energy evolution of the focused wave and its correlation with input parameters for the wave generation. The focused wave is numerically generated based on the fully nonlinear potential wave theory which is solved by the Quasi Arbitrary Lagrangian Eulerian-Finite Element Method. The investigation is performed by dividing the generated wave energy into three categories according to their frequency intervals, i.e., the initially assigned frequency interval [f1 fN], the frequencies lower (f < f1) and higher (f > fN) than the initial interval. The amount of the generated energy falling into three energy categories and the energy distribution in the initial frequency interval are analysed against amplitude parameters and frequency bands under three amplitude spectra. Four indicators are proposed to indicate the actual energy variations comparing to the initial design. It is found that for all the three frequency intervals the energies increase when the amplitude parameters increases or the given frequency shifts towards the lower frequency domain. The choice of wave amplitude spectrum plays a significant role to maintain the distribution of the energy in the design frequency range and to minimise the energies out of the design frequency range. The results from the second-order wave group theory are used to assist analyses of the mechanism of the energy evolution alongside the focused wave generation. It is found that the lower-frequency energy in the vicinity of the focusing point is dominated by the second-order difference waves, whereas the higher-frequency energy is mainly produced by the wave flap. The waves which are higher than the second-order and the complex interactions not considered by the second-order wave theory are found significantly disturbing the energy distribution in the originally assigned wave-frequency interval.

Publication Type: Article
Additional Information: © 2024 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license (
Publisher Keywords: Focused wave generation, Energy evolution, Wave amplitude spectrum
Subjects: Q Science > QC Physics
T Technology > TC Hydraulic engineering. Ocean engineering
Departments: School of Science & Technology
School of Science & Technology > Engineering
SWORD Depositor:
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Available under License Creative Commons: Attribution International Public License 4.0.

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