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Wave–current interaction has always been a challenging topic in fluid mechanics. The research on bimodal waves has received much more attention recently, but their evolutions influenced by underlying currents are not yet clear. This study aims to investigate the effects of co- and counter-propagating currents on spatial evolution using a fully nonlinear wave-current tank based on the high-order spectral method. The process of the wave focus is significantly shortened by the counter-propagating current, resulting in a sharper crest focus, followed by the trough focus. Concurrently, the decrease in the total envelope height and width is accelerated before wave focus and then the increase is decelerated, accompanied by a delay in the envelope profile transition from the backward-leaning to the forward-leaning. The co-propagating current exhibits the opposite phenomenon. The analysis of the spectral energy distribution aids in clarifying the variation of the envelope profile. The energy redistribution, characterized by a downshift of the frequency band, and a decreased energy distribution at the second peak, along with the slightly larger value of the root mean square frequency, indicates that the energy back-flow is obstructed by the counter-propagating current. These findings contribute to our understanding of the current effect on the focused double-wave-group, providing valuable insights for future research and applications in this field. [ABSTRACT FROM AUTHOR]

Enhancing the survival performance of wave energy converters (WECs) in extreme wave conditions is crucial, and reducing wave loads is a key aspect of this. Placing the device underwater has been recognized as a beneficial strategy, yet the determination of the optimal submerged depth and the effects of varying wave conditions remain ambiguous. To address this, the study numerically analyzes the total forces in both horizontal and vertical directions, along with their harmonic components, across different wave configurations. A computational fluid dynamics method is employed to investigate a triangular-baffle bottom-shaped oscillating floater, which is known for its high energy conversion efficiency. The findings indicate that submerging the device to a depth equivalent to half the actual focused amplitude (1/2Ab) is the most effective strategy in the given sea state, offering superior wave force reduction vertically and robust performance horizontally. The analysis of harmonics reveals the significant contribution of high-order components to the total wave forces. Additionally, the study examines the impact of focused wave amplitudes and peak frequencies, showing that although force reductions are lessened in more extreme conditions, the optimal submerged depth of 1/2Ab still yields near 30% reduction in total vertical force and 22% in total horizontal force. This research provides theoretical insight that can guide the enhancement of WECs' survival capabilities in practical engineering applications. [ABSTRACT FROM AUTHOR]

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]

Directional distribution is believed to have a significant impact on the statistical characteristics in multi-directional sea states. In real sea states, short-crested waves are discrete not only in frequency but also in direction. For the former one, they are well explained in unidirectional mode, but for the latter one, they are not. In this paper, the kurtosis of short-crested waves with equivalent energy is first discussed. Unimodal-spectrum-multi-direction sea states and bimodal-spectrum-multi-direction sea states are simulated for a long time in a numerical wave basin based on the high-order spectral method. In the equivalent sea-swell sea state, the spatial evolution of kurtosis becomes more inhomogeneous, along with the maximum value of kurtosis being larger and the area where the maximum value occurs wider in the configuration with a crossing angle β = 40° than that with β = 0°, while little variations in swell-dominated and wind-sea-dominated states. A positive linear correlation between wavelet group steepness and kurtosis is obtained in a unimodal sea state, but not applied to a crossing sea state characterized by a bimodal spectrum. The exceedance probability of wave height and wave crest distribution at maximum kurtosis is also given. These findings can help predict the probability of extreme waves occurring, guiding the selection of ocean engineering sites to avoid extreme configurations. [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]

Nonlinear interactions in wave-group focusing are regarded as one of the main mechanisms in the generation of destructive extreme waves. In real seas, the wideband bimodal state is a typical configuration, containing interactions within a single wave group and between different wave groups. The former has been well uncovered under the assumption of narrow bandwidth, but the latter is poorly understood. In this paper, physical experiments are conducted to reveal the physics of double-wave-group focusing considering various energy distributions. Superposed wavemaker signals generated by the iteration method are applied to produce a double-wave-group focusing with the interactions being decomposed. Results of the wavelet-based bicoherence spectrum show that double-wave-group focusing is distinguished from the linear superposition of two single-wave-group focusing mainly in the nonlinear interactions induced by the second-order sum harmonics. Under the assumption of equivalent energy, interactions of the second-order sum harmonics between the lower frequency group and higher frequency group cannot be ignored in swell-dominated states, and lesser linear interactions and stronger nonlinear interactions are observed while the spectral distribution of the double-wave-group is more asymmetrical. This work is anticipated to contribute to the understanding of the generation mechanism of extreme waves driven by strong nonlinearity. [ABSTRACT FROM AUTHOR]

A hybrid system integrating a power take-off (PTO) system into a floating breakwater is a promising candidate for both shoreline protection and commercial wave energy extraction. Although geometric asymmetry is important to such PTO-integrated breakwaters, its role in energy conversion efficiency and wave attenuation is poorly understood. In this study, a two-dimensional semi-analytical model dealing with floats with arbitrary bottom shapes is established based on the potential flow theory. To quantify the geometric asymmetry reflected by PTO-integrated breakwaters with different contours, the degree of asymmetry and the absolute asymmetry are newly defined mathematically. A set of symmetric and asymmetric PTO-integrated breakwaters are comparatively studied to demonstrate the effect of linear PTO damping and geometric asymmetry on the transmission coefficient, the reflection coefficient, and the energy conversion efficiency. Results show that no matter the hybrid system is symmetric or asymmetric, a larger PTO damping is beneficial for wave attenuation in longer waves, particularly at the heaving natural period of the device. On the premise that the PTO damping is optimized, an increase in the degree of asymmetry greatly improves the energy conversion efficiency. An increase in the absolute asymmetry slightly improves wave attenuation. • Interactions between waves and a float with arbitrary bottom shapes are modeled. • Installing a power take-off (PTO) on a breakwater improves its wave attenuation. • The degree of asymmetry (DoA) of a float is newly defined mathematically. • DoA greatly influences PTO-integrated breakwater's energy conversion efficiency. • DoA slightly influences PTO-integrated breakwater's wave attenuation. [ABSTRACT FROM AUTHOR]