Unified analytical solution for group-induced infragravity waves based on Green's function
Unified analytical solution for group-induced infragravity waves based on Green's function
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DOI：
10.1017/jfm.2023.475
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发表时间：
2023-07
影响因子：
3.7
通讯作者：
Zhiling Liao;Q. Zou;Ye Liu;S. Contardo;Shaowu Li
中科院分区：
文献类型：
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作者：
Zhiling Liao;Q. Zou;Ye Liu;S. Contardo;Shaowu Li
短波群强迫是亚重力波的主要驱动机制。在群速度等于浅水波传播速度的浅水中，对波群强迫的亚谐响应接近共振。目前，缺乏对自由分量和束缚分量之间的联系的理解，以及现有的解决方案之间的一致性，在中间和浅水区的非共振和近共振条件。本文首次基于绿色函数导出了群生次谐波的统一解。新的解决方案是有效的任何共振强度，并能够描述组诱导的次谐波行为在所有水深一致，从一个新的角度。所提出的解决方案简化为用于中间深度的现有解决方案（Longuet-Higgins & Stewart，J. Fluid Mech.，第13卷，1962年，第13页。481-504; Zou，Phys. Oceanogr.，第41卷，2011年，pp. 1842-1859）、浅水和/或在平面倾斜的海滩上（货车Leeuwen，PhD thesis，TU德尔夫特，1992; Schäffer，J. Fluid Mech.，第247卷，1993年，第247页。551-588; Janssen等人，J. Geophys.结果：第108卷，2003，第3252页; Contardo等人，海洋物理学杂志，第51卷，2021年，pp. 1465-1487; Liao等人，海洋物理学杂志，第51卷，2021年，pp. 2749-2765）。与以前的解决方案不同，绿色的功能为基础的解决方案描述了所有的次谐波作为自由的次谐波连续辐射远离每个点源在组诱导的强迫场确定的波辐射应力梯度。所有这些自由次谐波的叠加产生所谓的约束次谐波，由以前的研究，由于每个自由次谐波的组调制发射通过源场绑定到波群。因此，该解提供了理论证据，表明在任何观测点的群诱导次谐波是依赖于周围的辐射应力场和地形。在浅水中的全共振条件下，在所有源位置激发的下行波传播的次谐波相互干涉，因此，它们叠加的振幅与波群的行进距离成正比。结合传统的移动断点强迫模型，本文解预测的碎波带次谐波振幅与实验观测结果吻合较好。
Abstract Short-wave group forcing is a major driving mechanism of infragravity waves. The subharmonic response to wave group forcing approaches resonance in shallow water where the group velocity is equal to the shallow-water wave-propagating speed. Currently, there is a lack of understanding of the connection between the free and bound components of group-induced infragravity waves and the consistency among existing solutions for off- and near-resonance conditions in intermediate and shallow water. Here, a unified solution of group-induced subharmonics is derived based on Green's function for the first time. The new solution is valid for any resonance intensity and is able to describe group-induced subharmonic behaviour at all water depths consistently from a new angle. The proposed solution reduces to existing solutions for intermediate depth (Longuet-Higgins & Stewart, J. Fluid Mech., vol. 13, 1962, pp. 481–504; Zou, Phys. Oceanogr., vol. 41, 2011, pp. 1842–1859), shallow water and/or over a plane sloping beach (Van Leeuwen, PhD thesis, TU Delft, 1992; Schäffer, J. Fluid Mech., vol. 247, 1993, pp. 551–588; Janssen et al., J. Geophys. Res., vol. 108, 2003, p. 3252; Contardo et al., J. Phys. Oceanogr., vol. 51, 2021, pp. 1465–1487; Liao et al., J. Phys. Oceanogr., vol. 51, 2021, pp. 2749–2765). Unlike previous solutions, the Green's function-based solution describes all subharmonics as free subharmonics continuously radiated away from each point source in the group-induced forcing field determined by wave radiation stress gradients. The superposition of all these free subharmonics yields so-called bound subharmonics by previous studies due to group-modulated emission of each free subharmonic through the source field bound to the wave group. Therefore, this solution provides theoretical evidence that the group-induced subharmonic at any observation point is dependent on the surrounding radiation stress field and topography. Under full-resonance conditions in shallow water, downwave-propagating subharmonics excited at all source locations interfere with each other constructively; therefore, their superposed amplitude is proportional to the travel distance of wave groups. Combined with the conventional moving-breakpoint forcing model, the predicted amplitude of the subharmonic in the surf zone by the present solution is in good agreement with laboratory observations.