Abstract In this paper, the cross-shore propagation and shoaling of bound infragravity (IG) waves have been investigated. By establishing a conceptual 1D model utilizing a constant slope in the shoaling zone, a semi-analytical solution for bound IG waves could be obtained. Through the use of this semi-analytical solution, a collection of bichromatic conditions have been simulated, thus confirming the dependence of the forced long wave shoaling rate on a normalized bed slope β . β was found to be the dominant factor controlling the shoaling of bound long waves, yet when the bichromatic wave steepness become more significant (in this study around 0.10), the mean primary wave frequencies come into play. A detailed analysis confirmed an over-estimation of the equilibrium solution by Longuet-Higgins and Stewart (1960) (LHS60), which was derived based on a flat bottom in the first place. This over-estimation was found to be the most significant for primary short waves with a small wave steepness in the offshore region. A correction to the equilibrium solution of LHS60 has been derived, and its validity has been verified through a comparison to a high-resolution laboratory experiment under bichromatic wave conditions. Furthermore, the phase shift between the short wave groups and the IG waves has been discussed. At the innermost of the shoaling zone, the bound IG waves phases are still found to be strongly governed by the local forcing of short wave groups, as has been pointed out by Baldock (2006). For the near-resonant case, the bound IG waves are anti-phase to the short wave groups, and a larger phase shift in the shoaling zone might be the result of superposition of incoming free IG waves.

中文翻译：

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双色波条件下平面斜坡上束缚次引力波的浅滩化

摘要 在本文中，研究了束缚超重力（IG）波的跨岸传播和浅滩。通过在浅滩区建立一个利用恒定斜率的概念性一维模型，可以获得约束 IG 波的半解析解。通过使用这种半解析解，模拟了一系列双色条件，从而证实了受迫长波浅滩率对归一化床坡度 β 的依赖性。发现 β 是控制束缚长波浅滩的主要因素，但当双色波陡度变得更加显着（在本研究中约为 0.10）时，平均主波频率开始发挥作用。详细分析证实了 Longuet-Higgins 和 Stewart (1960) (LHS60) 对平衡解的高估，这首先是基于平底推导出来的。发现这种高估对于近海地区具有小波陡度的初级短波最为显着。已推导出对 LHS60 平衡解的修正，并通过与双色波条件下的高分辨率实验室实验进行比较，验证了其有效性。此外，还讨论了短波群和 IG 波之间的相移。正如 Baldock (2006) 所指出的那样，在浅滩区的最内部，仍然发现束缚 IG 波相位受到短波群的局部强迫的强烈控制。对于近谐振情况，束缚 IG 波与短波群反相，