Modulation Instability of Hydro-Elastic Waves Blown by a Wind with a Uniform Vertical Profile

Boral, Susam and Sahoo, Trilochan and Stepanyants, Yury ORCID: https://orcid.org/0000-0003-4546-0310 (2021) Modulation Instability of Hydro-Elastic Waves Blown by a Wind with a Uniform Vertical Profile. Fluids, 6 (12):458. pp. 1-18.

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Abstract

An interesting physical phenomenon was recently observed when a fresh-water basin is covered by a thin ice film that has properties similar to the property of a rubber membrane. Surface waves can be generated under the action of wind on the air–water interface that contains an ice film. The modulation property of hydro-elastic waves (HEWs) in deep water covered by thin ice film blown by the wind with a uniform vertical profile is studied here in terms of the airflow velocity versus wavenumber. The modulation instability of HEWs is studied through the analysis of coefficients of the nonlinear Schrödinger (NLS) equation with the help of the Lighthill criterion. The NLS equation is derived using the multiple scale method in the presence of airflow. It is demonstrated that the potentially unstable hydro-elastic waves with negative energy appear for relatively small wind speeds, whereas the Kelvin–Helmholtz instability arises when the wind speed becomes fairly strong. Estimates of parameters of modulated waves for the typical conditions are given.


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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Faculty/School / Institute/Centre: Historic - Faculty of Health, Engineering and Sciences - School of Sciences (6 Sep 2019 - 31 Dec 2021)
Faculty/School / Institute/Centre: Historic - Faculty of Health, Engineering and Sciences - School of Sciences (6 Sep 2019 - 31 Dec 2021)
Date Deposited: 07 Feb 2022 05:29
Last Modified: 03 Aug 2022 00:59
Uncontrolled Keywords: wind wave; ice cover; vortex sheet; negative energy wave; modulation instability
Fields of Research (2008): 02 Physical Sciences > 0203 Classical Physics > 020303 Fluid Physics
01 Mathematical Sciences > 0102 Applied Mathematics > 010207 Theoretical and Applied Mechanics
Fields of Research (2020): 51 PHYSICAL SCIENCES > 5103 Classical physics > 510301 Acoustics and acoustical devices; waves
49 MATHEMATICAL SCIENCES > 4901 Applied mathematics > 490109 Theoretical and applied mechanics
Socio-Economic Objectives (2008): E Expanding Knowledge > 97 Expanding Knowledge > 970102 Expanding Knowledge in the Physical Sciences
E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences
Socio-Economic Objectives (2020): 28 EXPANDING KNOWLEDGE > 2801 Expanding knowledge > 280120 Expanding knowledge in the physical sciences
28 EXPANDING KNOWLEDGE > 2801 Expanding knowledge > 280118 Expanding knowledge in the mathematical sciences
Identification Number or DOI: https://doi.org/10.3390/fluids6120458
URI: http://eprints.usq.edu.au/id/eprint/46088

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