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The Effect of Random Wind Forcing in the Nonlinear Schrödinger Equation

Institute of Mechanics and Ocean Engineering, Hamburg University of Technology, 21073 Hamburg, Germany
Fluids 2019, 4(3), 121; https://doi.org/10.3390/fluids4030121
Received: 5 May 2019 / Revised: 21 June 2019 / Accepted: 25 June 2019 / Published: 2 July 2019
(This article belongs to the Special Issue Nonlinear Wave Hydrodynamics)
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Abstract

The influence of a strong and gusty wind field on ocean waves is investigated. How the random wind affects solitary waves is analyzed in order to obtain insights about wave generation by randomly time varying wind forcing. Using the Euler equations of fluid dynamics and the method of multiple scales, a random nonlinear Schrödinger equation and a random modified nonlinear Schrödinger equation are obtained for randomly wind forced nonlinear deep water waves. Miles theory is used for modeling the pressure variation at the wave surface resulting from the wind velocity field. The nonlinear Schrödinger equation and the modified nonlinear Schrödinger equation are computed using a relaxation pseudo spectral scheme. The results show that the influence of gusty wind on solitary waves leads to a randomly increasing ocean wave envelope. However, in a laboratory setup with much smaller wave amplitudes and higher wave frequencies, the influence of water viscosity is much higher. This leads to fluctuating solutions, which are sensitive to wind forcing. View Full-Text
Keywords: surface gravity waves; random wind-wave interactions; rogue waves; modified nonlinear Schrödinger equation; stochastic partial diferential equations surface gravity waves; random wind-wave interactions; rogue waves; modified nonlinear Schrödinger equation; stochastic partial diferential equations
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Dostal, L. The Effect of Random Wind Forcing in the Nonlinear Schrödinger Equation. Fluids 2019, 4, 121.

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