水深地形上长波的自感应透明：色散冲击机制
Self-induced transparency of long water waves over bathymetry: the dispersive shock mechanism
AI总结：
研究长波在变水深地形上的传播，发现色散冲击波使能量转向高波数带，实现自感应透明，透射率依赖振幅与距离，影响海啸危害评估。
摘要：
色散冲击波（DSW）是长波的一个显著特征，常在潮涌和 tsunami/meteotsunami 情境中观察到。它们与水深地形的相互作用尚不为人所知。海啸和气象海啸对海岸线的危害关键取决于穿过近岸浅水架的入射能量通量比例。在此，通过在 Boussinesq 方程框架内考虑变深度上的波浪非线性动力学，我们表明透射能量通量比例可以强烈依赖于入射波的初始振幅及其传播距离。该现象类似于非线性光学中的自感应透明：小振幅波被水深地形不均匀性反射，而较大振幅的波则通过。长波自感应透明的机制可解释如下。在线性设置中，长度与入射波长相当的水深地形不均匀性通过透射高波数分量起到高通滤波器的作用。DSW 演化有效地将波能转移到高波数带，在该带中反射可忽略不计。通过检查一个理想化的水深地形模型，我们表明这是一个一阶效应，并探讨了其在与气象海啸相关的参数范围内的依赖性。由于与 DSW 无关的束缚谐波增长而导致的波能向高波数带的转移作用被发现是小的。
英文摘要：
Dispersive shock waves (DSW) are a salient feature of long water waves often observed in tidal bores and tsunami/meteotsunami contexts. Their interaction with bathymetry is poorly understood. The shoreline hazard from tsunamis and meteotsunamis critically depends on the fraction of incoming energy flux transmitted across the shallow nearshore shelf. Here, by considering nonlinear dynamics of waves over variable depth within the framework of the Boussinesq equations we show that the transmitted energy flux fraction can strongly depend on the initial amplitude of the incoming wave and the distance it travels. The phenomenon is similar to self-induced transparency in nonlinear optics: small amplitude waves are reflected by bathymetry inhomogeneity, while a larger amplitude ones pass through. The mechanism of self-induced transparency of long water waves can be explained as follows. In linear setting a bathymetry inhomogeneity, of length comparable to that of the incident wavelength, by transmitting high wavenumber components acts as a high-pass filter. The DSW evolution efficiently transfers wave energy into high wavenumber band, where reflection is negligible. By examining an idealized model of bathymetry we show that this is an order one effect and explore its dependence on parameters in the range relevant for meteotsunamis. The role of wave energy transfer into high wavenumber band owing to the growth of bound harmonics unrelated to the DSW was found to be small.
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