The effect of random wind forcing in the nonlinear Schrödinger equation
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.
surface gravity waves
random wind-wave interactions
modified nonlinear Schrödinger equation
stochastic partial diferential equations