Energy transfer in the spatial evolution of double-wave-group focusing

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

Wave attenuation and focusing performance of parallel twin parabolic arc floating breakwaters

The hybrid system consisting of floating breakwater and point absorber wave energy converters provides a promising solution for shoreline protection and wave power generation. In the hybrid system, the breakwater plays an important role in protecting the sheltered area on the lee side and focusing high waves for better energy harvesting on the weather side. To improve the wave attenuation and focusing performance, a twin-breakwater consisting of a pair of parallel parabolic pontoons is proposed. Based on the potential flow theory of linear waves, the influences of gap width and connection method applied between the two pontoons are studied in the frequency domain, with an emphasis on the so-called critical mode around which both wave attenuation and focusing could be improved. Results show that the rigidly connected twin-breakwater is superior to the unconnected twin-breakwater with the same configuration in both wave attenuation and focusing. A second critical mode with lower frequency is also found under particular gap width, providing a potential for the defense of long waves. An optimal attenuation could be obtained by applying a proper gap width

Influence of uniform currents on nonlinear characteristics of double-wave-group focusing

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

Hydrodynamic performance of a dual-floater hybrid system combining a floating breakwater and an oscillating-buoy type wave energy converter

The high cost of power generation impedes commercial-scale wave power operations. The objective of this work is to provide a cost-sharing solution by combining wave energy extraction and coastal protection. A two-dimensional numerical wave tank was developed using Star-CCM+ Computational Fluid Dynamics software to investigate the hydrodynamic performance of a dual-floater hybrid system consisting of a floating breakwater and an oscillating-buoy type wave energy converter (WEC), and was compared with published experimental results. The differences between the hydrodynamic performance of the hybrid system, a single WEC and a single breakwater were compared. Wave resonance in the WEC-breakwater gap has a significant impact on system performance, with the hybrid system demonstrating both better wave attenuation and wave energy extraction capabilities at low wave frequencies, i.e., wider effective frequency. Forces on the breakwater were generally reduced due to the WEC. Wave resonance in the narrow gap has an adverse effect on the energy efficiency of the hybrid system with an asymmetric WEC, while a beneficial effect with a symmetric WEC. The wave energy conversion efficiency of hybrid system can be improved by increasing the draft and width of the WEC and decreasing the distance between the WEC and the breakwater. The findings of this paper make wave energy economically competitive and commercial-scale wave power operations possible

Hydrodynamic performance of a dual-floater hybrid system combining a floating breakwater and an oscillating-buoy type wave energy converter

The high cost of power generation impedes commercial-scale wave power operations. The objective of this work is to provide a cost-sharing solution by combining wave energy extraction and coastal protection. A two-dimensional numerical wave tank was developed using Star-CCM+ Computational Fluid Dynamics software to investigate the hydrodynamic performance of a dual-floater hybrid system consisting of a floating breakwater and an oscillating-buoy type wave energy converter (WEC), and was compared with published experimental results. The differences between the hydrodynamic performance of the hybrid system, a single WEC and a single breakwater were compared. Wave resonance in the WEC-breakwater gap has a significant impact on system performance, with the hybrid system demonstrating both better wave attenuation and wave energy extraction capabilities at low wave frequencies, i.e., wider effective frequency. Forces on the breakwater were generally reduced due to the WEC. Wave resonance in the narrow gap has an adverse effect on the energy efficiency of the hybrid system with an asymmetric WEC, while a beneficial effect with a symmetric WEC. The wave energy conversion efficiency of hybrid system can be improved by increasing the draft and width of the WEC and decreasing the distance between the WEC and the breakwater. The findings of this paper make wave energy economically competitive and commercial-scale wave power operations possible

Hydrodynamic performance of a floating breakwater as an oscillating-buoy type wave energy converter

Combined floating breakwater and wave energy converter systems have the potential to provide a cost-effective solution to offshore power supply and coastal protection. This will make wave energy economically competitive and commercial-scale wave power operations possible. This paper investigates the hydrodynamic features of wave energy converters that meet the dual objectives of wave energy extraction and attenuation for such a combined system. A two-dimensional numerical model was established using Star-CCM+ commercial software based on viscous Computational Fluid Dynamics theory to investigate the hydrodynamic performance of an oscillating buoy Wave Energy Converter (WEC) type floating breakwater under regular waves. The model proposed in this paper was verified with published experimental results. The hydrodynamics of symmetric and asymmetric floaters were investigated to demonstrate their wave attenuation and energy extraction performance, including square bottomed, triangular bottomed (with and without a baffle plate), and the Berkley Wedge. The asymmetric floaters were found to have higher power conversion efficiency and better wave attenuation performance, especially the Berkeley Wedge bottom device and the triangular-baffle bottom device. The triangular-baffle bottom device with a simpler geometry achieved similar wave attenuation and energy extraction performance characteristics to that of the Berkeley Wedge device. The maximum energy conversion efficiency of the triangular-baffle bottom floater reached up to 93%, an impressive WEC device among many designs for wave energy conversion. There may be a great potential for this newly proposed triangular-baffle bottom WEC type of floater to be an ideal coastal structure for both coastal protection and wave energy extraction

Effects of narrow gap wave resonance on a dual-floater WEC-breakwater hybrid system

The effects of gap wave resonance on the performance of a dual-floater hybrid system consisting of an oscillating-buoy type wave energy converter (WEC) and a floating breakwater are important for the design of such a hybrid system. This paper investigates the gap wave resonance by employing a two-dimensional numerical wave flume developed using the Star-CCM + software. The maximum wave elevation in the WEC-breakwater gap and the effects of the gap wave resonance on the performance of the dual-floater hybrid system were studied. The influence of the WEC motion and the geometrical parameters of the hybrid system on the maximum wave elevation were analyzed. The maximum gap wave elevation is essentially controlled by the vertical velocity of the free surface in the WEC-breakwater gap. The gap wave resonance was found to significantly improve the wave energy extraction performance of the hybrid system. This allowed the maximum conversion efficiency to exceed the well-known limit of 0.50 for a symmetric body in single degree-of-freedom motion. The wave resonance frequencies in the WEC-breakwater gap decreased with the increase of the gap width and the WEC draft. Due to the energy extraction of the WEC, the horizontal and vertical forces on the breakwater were reduced by up to 0.79 and 0.59, respectively

Nonlinear statistical characteristics of the multi-directional waves with equivalent energy

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

Frequency domain analysis of a hybrid aquaculture-wind turbine offshore floating system

The aquaculture industry is being pushed into deeper waters, to accommodate the increasing demand for seafood worldwide and the lack of nearshore sites: aquaculture systems for farther, harsher conditions are now being proposed. The Blue Growth initiative by the European Union is also tuned in the same direction, with the focus being on developing ocean based resources, including energy and aquaculture, and finding synergies among them. The present work proposes a novel multi-purpose platform (MPP), by retrofitting a feed barge with a small wind turbine and energy storage system, able to provide sustainable energy to a reference offshore aquaculture farm. The requirements and constraints for such hybrid system are defined, as well as a set of keys load cases, and its performance are analysed in the frequency domain. Wave loads are modelled using linear potential theory, while from an aerodynamic point of view, only the maximum thrust at the wind turbine hub level is considered in the static stability analysis. With reference to stability criteria and dynamic analysis in frequency domain, the suitability of the proposed MPP to act as a source of feed storage and energy supply is established, showing this as a potentially suitable solution