Modulation Instability of Surface Waves in the Model with the Uniform Wind Profile

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