Long wave propagation and run-up in converging bays
Long wave propagation and run-up in converging bays
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会聚湾中的长波传播和上升
DOI：
10.1017/jfm.2016.327
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发表时间：
2016
影响因子：
3.7
通讯作者：
T. Shimozono
中科院分区：
文献类型：
--
作者：
T. Shimozono
推导了描述二维波浪在收敛海湾中演化的解析解。研究了三种不同断面的海湾类型：U形海湾、V形海湾和尖形海湾。对于这些海湾，二维线性浅水方程可以减少到一维线性色散波方程，如果横向流加速度在他们被假定为小。导出的解的特征在于，由于波折射的二维高阶修正的领先阶平面波解。三种海湾类型的波浪振幅纵向上以不同的速率增加，而在横向上表现出弱的抛物线变化。波浪折射显著影响相对较短的波浪，有助于以不同的方式将波浪能量传递到内湾，具体取决于海湾类型。对甚高阶波单元的摄动分析表明，只有当海湾宽度与波长的比值小于某一极限时，解才有效，该极限因海湾类型而异。超过极限，高阶效应不再是一个小的修正，这意味着波的行为成为高度二维的，并可能导致全反射。结果表明，在该解的适用范围内，高阶项对湾头处的爬高影响很小，忽略横向流的爬高公式具有广泛的适用性。本文还讨论了波浪破碎对爬高的限制。
Analytical solutions are derived to describe two-dimensional wave evolution in converging bays. Three bay types of different cross-sections are studied: U-shaped, V-shaped and cusped bays. For these bays, the two-dimensional linear shallow water equations can be reduced to one-dimensional linear dispersive wave equations if the transverse flow acceleration inside them is assumed to be small. The derived solutions are characterized as the leading-order plane-wave solutions with higher-order corrections for two-dimensionality due to wave refraction. Wave amplitude longitudinally increases with different rates for the three bay types, whereas it exhibits weak parabolic variations in the transverse direction. Wave refraction significantly affects relatively short waves, contributing to wave energy transfer to the inner bay in a different manner depending on the bay type. The perturbation analysis of very high-order wave celerity suggests that the solutions are valid only when the ratio of the bay width to the wavelength is smaller than a certain limit that differs with bay type. Beyond the limit, the higher-order effect is no longer a minor correction, implying that wave behaviours become highly two-dimensional and possibly cause total reflection. The higher-order effect on the run-up height at the bay head is found to be small within the applicable range of the solution, and thus, the run-up formula neglecting the transverse flows has a wide validity. We also discuss the limitation of run-up height by wave breaking on the basis of a breaking criterion from previous studies.