The modulation instability of surface capillary-gravity water waves is analysed in a shear flow model with a tangential discontinuity of velocity. It is assumed that air blows along the surface of the water with a uniform profile in the vertical direction. Such a model, despite its simplicity, plays an important role in hydrodynamics as the reference model for investigating basic physical phenomena of wave–current interactions and acquiring insights into a series of complex phenomena. In certain cases where the wavelength of interfacial perturbations is much bigger than the width of the shear flow profile, the model with the tangential discontinuity in the velocity is adequate for describing physical phenomena at least within limited spatial and temporal frameworks. A detailed analysis of the air-flow conditions under which modulation instability sets in is presented. It is also shown that the interfacial waves are subject to dissipative or radiative instability when negative-energy waves appear at the interface.

中文翻译：

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具有均匀风廓线的模型中表面波的调制不稳定性

在切向速度不连续的剪切流模型中分析了表面毛细管重力水波的调制不稳定性。假定空气沿着水表面在垂直方向上以均匀的轮廓吹动。这种模型尽管简单，但在流体力学中起着重要的作用，它是研究波流相互作用的基本物理现象并获得对一系列复杂现象的见解的参考模型。在某些情况下，界面扰动的波长远大于剪切流剖面的宽度，速度切线不连续的模型足以描述至少在有限的空间和时间框架内的物理现象。给出了调制不稳定性所处的气流条件的详细分析。还显示出，当界面处出现负能量波时，界面波会发生耗散或辐射不稳定性。