Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

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

Version 1 : Received: 18 March 2021 / Approved: 22 March 2021 / Online: 22 March 2021 (11:26:38 CET)

A peer-reviewed article of this Preprint also exists.

Boral, S.; Sahoo, T.; Stepanyants, Y. Modulation Instability of Surface Waves in the Model with the Uniform Wind Profile. Symmetry 2021, 13, 651. Boral, S.; Sahoo, T.; Stepanyants, Y. Modulation Instability of Surface Waves in the Model with the Uniform Wind Profile. Symmetry 2021, 13, 651.

Journal reference: Symmetry 2021, 13, 651
DOI: 10.3390/sym13040651

Abstract

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 fow 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 negativeenergy waves appear at the interface.

Subject Areas

Two-layer fluid; shear flow; air-water interface; surface tension; vortex sheet; Kelvin-Helmholtz instability; negative-energy wave; modulation instability

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