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The linear superposition of the individual wave groups underestimates the bimodal waves, as it overlooks the interactions between these wave groups, which is thought to be connected to the generation of extreme waves. Continuing our previous work [Zhou et al., "Experimental study on the interactions between wave groups in double-wave-group focusing," Phys. Fluids 35(3), 037118 (2023)], the energy transfer in the spatial evolution of double-wave-group focusing is highlighted based on a fully nonlinear numerical wave tank with the high-order spectral method. The findings reveal that a sea state with a narrower intermodal distance or an uneven distribution of the bimodal spectrum tends to induce larger waves. The third-order nonlinear interaction is primarily triggered by the transient wave focusing, as opposed to a prolonged evolution like the behavior of even-order components. The configurations of the sea state exert varying impacts on the evolution of harmonical energy, with the most potent nonlinearity observed away from the actual focused position, the nonlinear energy amplified relative to the initial state, and the energy redistributed after wave focus. The study also uncovers that during the wave focus and defocus process, waves experience an irreversible energy exchange, with frequencies shifting from higher to lower, likely due to second-order harmonics. These discoveries broaden our comprehension of the nonlinear characteristics inherent in the interaction between the swell and wind-sea waves. [ABSTRACT FROM AUTHOR]

Current is considered to be a crucial environmental factor in producing extreme waves. The study of nonlinear characteristics in wave–current interactions has been explored, but the role of currents in the more complex interaction processes of double-wave-group focusing is not yet known. Based on our previous research about the nonlinear interactions between wave groups, the impact of uniform current on nonlinear characteristics of double-wave-group focusing is to be investigated in this paper. A fully nonlinear numerical model using the high-order spectral method is developed to simulate various currents interacting with focused bimodal waves. Three ranges of variation exist: strongly opposing current, weakly opposing current, and following current. Unlike the conclusion in the unimodal waves, the asymmetries of the wave crest and that of the wave envelope influenced by currents are not synchronous, which is explained by the changes in the asymmetry of the secondary crests received energy from the currents, in addition to those of the magnitude of the maximum crest and the adjacent secondary crests. When opposing currents enhance to a certain level, a dynamic equilibrium between the energy of waves and currents would be achieved, in which the proportion of the linear components to their own is almost equivalent to that in the non-current state, revealing that the majority of nonlinearity generated by wave–current interaction is blocked at that time. These findings can promote an understanding of nonlinear characteristics due to wave–current interactions. [ABSTRACT FROM AUTHOR]

The problem of wave interaction with multiple adjacent floating solar panels with arbitrary types and numbers of constraints is considered. All the solar panels are assumed to be homogeneous, with the same physical properties, as well as modeled by using the Kirchhoff-Love plate theory. The motion of the fluid is described by the linear velocity potential theory. The domain decomposition method is employed to obtain the solutions. In particular, the entire fluid domain is divided into two types, the one below the free surface, and the other below elastic plates. The velocity potential in the free surface domain is expressed into a series of eigenfunctions. By contrast, the boundary integral equation and the Green function are employed to construct the velocity potential of fluid beneath the entire elastic cover, with unknowns distributed along two interfaces and jumps of physical parameters of the plates. All these unknowns are solved from the system of linear equations, which is established from the matching conditions of velocity potentials and edge conditions. This approach is confirmed with much higher computational efficiency compared with the one only involving eigenfunction expansion for the fluid beneath each plate. Extensive results and discussions are provided for the reflection and transmission coefficients of water waves, maximum deflection, and principal strain of the elastic plates; especially, the influence of different types and numbers of edge constraints are investigated in detail. [ABSTRACT FROM AUTHOR]

Predicting extreme waves can foresee the hydrodynamic environment of marine engineering, critical for avoiding disaster risks. Till now, there are barely any available models that can rapidly and accurately predict the occurrence probability of freak waves in a given state. This paper develops a trained model based on the Back Propagation (BP) neural network, with wave parameters of unidirectional sea state fed into the model, such as significant wave height, wave period, spectral type, and the intermodal distance of the peak frequencies. A rapid and accurate model optimized for predicting the occurrence probability of freak waves in a unidirectional sea state, from unimodal to bimodal configuration, is achieved by iterating to reduce accumulation errors. Compared to the regression and least-squares boosting trees, the optimized model performs much better in accurately predicting the occurrence probability of freak waves. Irrespective of whether in unimodal or bimodal sea state, this optimized model is competitive in calculation accuracy compared to theoretical models such as Rayleigh prediction and MER prediction, improved by at least 41%. The established model based on the BP neural network can quickly predict the threshold of freak waves in a given sea state, guiding practical engineering applications. [ABSTRACT FROM AUTHOR]

Integrating point absorber wave energy converters (PAWECs) and an offshore floating wind platform provide a cost-effective way of joint wind and wave energy exploitation. However, the coupled dynamics of the complicated hybrid system and its influence on power performance are not well understood. Here, a frequency-domain-coupled hydrodynamics, considering the constraints and the power output through the relative motion between the PAWECs and the semi-submersible platform, is introduced to optimize the size, power take-off damping, and layout of the PAWECs. Results show that the annual wave power generation of a PAWEC can be improved by 30% using a 90° conical or a hemispherical bottom instead of a flat bottom. Additionally, while letting the PAWECs protrude out the sides of the triangular frame of the platform by a distance of 1.5 times the PAWEC radius, the total power generation can be improved by up to 18.2% without increasing the motion response of the platform. The PAWECs can reduce the resonant heave motion of the platform due to the power take-off damping force. This study provides a reference for the synergistic use of wave and wind energy. [ABSTRACT FROM AUTHOR]