Abstract
An analytical solution for long waves propagating over a submerged atoll is established. The atolls involved in this study are annular coral reefs with large lagoons in the middle, and the expression of the cross section is a trinomial function of the radial distance, i.e., h=ar2s−brs+h0, where s is the positive rational number. This analytical solution extends the theory by Wang et al. (2018) as s is no longer limited to s=2/m, where m is the positive integer. In addition, by adjusting the terrain parameters properly, the analytic solution can be degenerated to describe the wave propagation over topography with a hump or pit. According to the relationship between wave rays and wave energy, the distribution characteristics and formation mechanism of energy over the topography are expounded. When the lagoon is non-existent, all wave rays converge at the x-axis, which results in an abrupt amplification of the wave amplitude around the convergence point. When a lagoon is mounted on the top of the atoll, the rays are scattered due to the refraction of the lagoon, and only some rays converge at the symmetrical axis and the ridges on both sides, which results in the amplification of wave amplitudes in these areas.
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ZHENG Jin-hai is an editorial board member of China Ocean Engineering and was not involved in the editorial review, or the decision to publish this article. All authors declare that there are no other competing interests.
Foundation item: This work was financially supported by Hainan Provincial Natural Science Foundation of China (Grant No. 422MS090), Fujian Provincial Natural Science Foundation Project of China (Grant No. 2022J05282) and 2020 Xiamen Youth Innovation Fund Project of China (Grant No.3502Z20206069).
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Fu, Dj., Liu, Bj., Zheng, Jh. et al. Study on the Propagation and Focusing Mechanism of Long Waves over A Submerged Atoll. China Ocean Eng 37, 204–217 (2023). https://doi.org/10.1007/s13344-023-0019-1
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DOI: https://doi.org/10.1007/s13344-023-0019-1