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.
Highlights
The formation of water waves under the influence of wind is an important physical process, which can result in the emergence of rogue waves
It can be further shown that weakly nonlinear solutions of the Euler equations can be reduced to solutions described by a complex envelope, which satisfies the nonlinear Schrödinger equation (NLS) in the case of one spatial dimension or in general to the
This work is organized as follows: after the introduction, a forced modified nonlinear Schrödinger equation for time and space variant wind-induced pressure is stated in Section 2; the numerical solution method for the evolution equations from Section 2 is presented in Section 3, followed by a description of the modeling and generation of a random wind velocity field in Section 4; in Section 5, the obtained results are presented and discussed; followed by the conclusions in the last Section
Summary
The formation of water waves under the influence of wind is an important physical process, which can result in the emergence of rogue waves. The role of randomness in the forcing of nonlinear waves was studied In this case it was of interest whether gusty wind leads to the development of large waves or whether it prevents the occurence of such waves. Using the method of multiple scales, Leblanc [14] derived a forced NLS for the case of deterministic wind forcing for weakly nonlinear surface gravity waves. This work is organized as follows: after the introduction, a forced modified nonlinear Schrödinger equation for time and space variant wind-induced pressure is stated in Section 2; the numerical solution method for the evolution equations from Section 2 is presented, followed by a description of the modeling and generation of a random wind velocity field in Section 4; in Section 5, the obtained results are presented and discussed; followed by the conclusions in the last Section This work is organized as follows: after the introduction, a forced modified nonlinear Schrödinger equation for time and space variant wind-induced pressure is stated in Section 2; the numerical solution method for the evolution equations from Section 2 is presented in Section 3, followed by a description of the modeling and generation of a random wind velocity field in Section 4; in Section 5, the obtained results are presented and discussed; followed by the conclusions in the last Section
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