Specific solutions of the nonlinear Schrödinger equation, such as the Peregrine breather, are considered to be prototypes of extreme or freak waves in the oceans. An important question is, whether these solutions also exist in the presence of gusty wind. Using the method of multiple scales, a nonlinear Schrödinger equation is obtained for the case of wind forced weakly nonlinear deep water waves. Thereby, the wind forcing is modeled as a stochastic process. This leads to a stochastic nonlinear Schrödinger equation, which is calculated for different wind regimes. For the case of wind forcing which is either random in time or random in space, it is shown that breather type solutions such as the Peregrine breather occur even in strong gusty wind conditions.
The dynamics of a novel wave energy converter based on a guided inclined point absorber are investigated. Thereby, it is studied through simulations and experiments whether different inclination angles of the guided point absorber lead to larger motion amplitudes and velocities in regular and irregular waves, from which energy can be harvested. For that, different simulations and experimental setups are analyzed in the presence of wave forcing. In the case of irregular waves a random non-white Gaussian stochastic process based on a sea spectrum is used. It is shown that the inclination angle has a significant influence on the energy harvesting output. Based on this insight, a simple control strategy is introduced in order to further increase the energy harvesting output.
The nonlinear Schrödinger equation plays an important role in wave theory, nonlinear optics and Bose-Einstein condensation. Depending on the background, different analytical solutions have been obtained. One of these solutions is the soliton solution. In the real ocean sea, interactions of different water waves can be observed at the surface. Therefore the question arises, how such nonlinear waves interact. Of particular interest is the interaction, also called collision, of solitons and solitary waves. Using a spectral scheme for the numerical computation of solutions of the nonlinear Schrödinger equation, the nonlinear wave interaction for the case of soliton collision is studied. Thereby, the influence of an initial random wave is studied, which is generated using a Pierson-Moskowitz spectrum.
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