Wave Energy Input Research Articles

Hybrid Torque Coefficient Control of Average-to-Peak Ratio for Turbine Angular Velocity Reduction in Oscillating-Water-Column-Type Wave Energy Converter

Wave energy converters (WECs) have significant potential to meet the increasing energy demands and using an oscillating water column (OWC) is one of the most reliable ways to implement them. The OWC has a simple structure and excellent durability. However, control of the power take-off (PTO) system is difficult due to variability in the input wave energy. In particular, the design and control of the PTO system are complex, as the average-to-peak ratio of the output generation is large. Owing to the nature of the OWC, if the energy above the rating cannot be controlled, the power generated is inevitably reduced due to the decrease in operating time. We propose a method to reduce the angular speed of the turbine by dividing the section according to the input energy and correspondingly changing the torque coefficient, thereby increasing the operating time of the OWC. The control methods for the PTO system of OWC are verified through a 30 kW full-scale experimental device to be installed in a real sea area. The full-scale experimental device consists of an inverter that simulates the mechanical torque of an OWC based on the aerodynamic simulation of an impulse turbine, an induction motor, a permanent magnet synchronous generator, an AC/DC converter, and a battery for the energy storage system. The performance of conventional control methods and the proposed method are compared based on the results of numerical simulations and experiments. We show that the fluctuation in the turbine angular velocity in the proposed method is significantly reduced compared with that in the conventional control methods under regular and irregular wave conditions.

Near‐Inertial Wave Propagation in the Deep Canadian Basin: Turning Depths and the Homogeneous Deep Layer

AbstractThe internal wave climate in the deep Arctic Ocean, away from the shelves, is quiet because the ice cover shields the ocean from wind energy input, and tidal amplitudes are small. Hence, mixing due to internal wave breaking is small. The shrinking Arctic sea ice cover, however, exposes more open ocean areas to energy transfer by wind. Consequently, more energetic near‐inertial internal waves (NIWs) may carry energy to the bottom, potentially enhancing deep mixing. In the deep Canadian Basin, weakly stratified layers with local buoyancy frequencies smaller than the wave frequency may prevent NIW propagation to the seafloor. We estimate the distribution of these near‐inertial turning depths from temperature and salinity data of the years 2005–2014. Near‐inertial turning depths are ubiquitous in the deep Canadian Basin at ∼2,750 m depth, between 100 and 1,200 m above the bottom. A deep homogeneous layer below 3,300 m is characterized by small squared buoyancy frequencies N2 ∼ 0 with locally unstable layers (N2 < 0). The turning depths reflect NIWs and hence limit their contribution to deep mixing, but the waves create an evanescent perturbation with exponentially decreasing amplitude that can interact with the bathymetry, especially above slopes and ridges where the height of the turning depths above the seafloor is small. After reflection, the main part of the wave energy is trapped between turning depths and the surface, so that a potential increase of wave energy input mainly affects mixing of mid‐depth water masses like the Atlantic Water.

Experimental investigation on multi-mode resonances in a rectangular harbor

Physical experiments were conducted to investigate the oscillations in a rectangular harbor for different modes with the same resonant frequency. Two multimode resonances, that is, case A for modes (0, 2) and (3, 1) and case B for modes (1, 1) and (2, 0) excited by bichromatic waves, were examined. The results showed that the multimode resonance was excited. During the response process when the resonance is initially excited, the subharmonic energy mainly focused on mode (0, 2) for case A and mode (2, 0) for case B. With the continuous input of wave energy, periodic modulations for the infragravity waves in the harbor were observed, implying that the subharmonic energy transfers freely between the two modes in a quasi-steady state. During the damping process, with no waves, the subharmonic energy returns to the mode that occupies the response process. The phenomenon that the subharmonic energy concentrates in the same mode in the response and damping processes is possibly because these modes are more easily excited than the others.

A Novel Wave Energy Equivalence Based Lumping Block Method for Efficiently Predicting the Fatigue Damage of Mooring Lines

The lumping block equivalent method (LBEM) is widely used to reduce the computational effort in the fatigue damage assessment of offshore structures, and the wave parameters of the representative sea states (RSSs) resulting from LBEM are of vital importance for the accurate prediction of offshore structures’ fatigue damage. In this study, a novel wave energy equivalence (WEE)-based LBEM is proposed to determine the wave parameters of the RSS accurately. The novelty of the proposed method is that a compact relationship between the input wave energy component and mooring lines’ fatigue damage is derived, and the modified statistical relationships between the wave parameters and spectral moments are provided by incorporating the effects of the peak enhancement factor of the input wave spectrum, the number of original sea states (OSSs) and the equivalence bandwidth of the OSSs. Based on the compact relationship, the wave energy component of the RSS can be determined from the wave energy component of the OSSs for each wave frequency from the viewpoint of the fatigue damage equivalence criterion. The wave energy distribution of the RSS can be accurately characterized with the wave energy distribution of the OSSs, and the spectral moments of the RSS can be calculated by its energy distribution directly, without any approximation. Moreover, the wave parameters of the RSS can be determined from the modified statistical relationships easily. The effectiveness of the proposed WEE LBEM is numerically investigated with a moored semi-submersible platform. Results show that the proposed WEE LBEM is robust, efficient and accurate within engineering expectations, and it outperforms the conventional LBEMs both in accuracy and robustness.

Effects of Breaking and Non‐Breaking Surface Wave Mixing on the Changjiang River Plume Dynamics in Summer

AbstractA wave‐current coupled model is implemented to investigate the impact of breaking and non‐breaking surface wave mixing on the structure and dynamics of the Changjiang River plume. Two main non‐breaking wave mixing schemes, modifying the turbulent viscosity directly versus adding wave‐induced turbulence production in the turbulence closure model, are incorporated to the Coupled Ocean‐Atmosphere‐WAVE‐Sediment Transport modeling system. Surface wave mixing typically thickens the plume and traps more freshwater in the near‐ and mid‐field regions. The surface turbulent kinetic energy produced by breaking waves corresponds to small wave energy input in fair weather conditions and has a moderate effect on the Changjiang River plume. In contrast, the addition of non‐breaking wave mixing enhances the turbulent viscosity roughly an order of magnitude in the surface layer. Simulations with non‐breaking wave mixing improve the representation of the plume structure compared to models without wave mixing or with only breaking wave mixing. The Changjiang River plume exhibits a north‐south asymmetry in both salinity and current field in summer. Further adding the non‐breaking wave mixing reduces the surface Ekman velocity and lowers the offshore plume expansion rate through interactions between the upwelling favorable winds and the Ekman layer depth. The resulting adjustment to the internal pressure gradient enhances the buoyancy current and magnifies the asymmetric structure of the Changjiang River plume in summer. While the two non‐breaking wave mixing schemes are conceptually different, our modeling experiments suggest that they have similar effects on the plume structure.

Deep Learning Prediction for Rotational Speed of Turbine in Oscillating Water Column-Type Wave Energy Converter

This study uses deep learning algorithms to predict the rotational speed of the turbine generator in an oscillating water column-type wave energy converter (OWC-WEC). The effective control and operation of OWC-WECs remain a challenge due to the variation in the input wave energy and the significantly high peak-to-average power ratio. Therefore, the rated power control of OWC-WECs is essential for increasing the operating time and power output. The existing rated power control method is based on the instantaneous rotational speed of the turbine generator. However, due to physical limitations, such as the valve operating time, a more refined rated power control method is required. Therefore, we propose a method that applies a deep learning algorithm. Our method predicts the instantaneous rotational speed of the turbine generator and the rated power control is performed based on the prediction. This enables precise control through the operation of the high-speed safety valve before the energy input exceeds the rated value. The prediction performances for various algorithms, such as a multi-layer perceptron (MLP), recurrent neural network (RNN), long short-term memory (LSTM), and convolutional neural network (CNN), are compared. In addition, the prediction performance of each algorithm as a function of the input datasets is investigated using various error evaluation methods. For the training datasets, the operation data from an OWC-WEC west of Jeju in South Korea is used. The analysis demonstrates that LSTM exhibits the most accurate prediction of the instantaneous rotational speed of a turbine generator and CNN has visible advantages when the data correlation is low.

Enhancement of dynamic performance of wave energy converter by introducing a flow control

The stabilization of power take-off (PTO) is imperative especially under circumstances of fluctuating input wave energy. In this paper, a flow control valve is introduced to optimize the transient process of the hydraulic PTO, which can contribute to a quicker adjustment and a stronger stability. Under variations of input power and load torque in transient process, an open-loop control method and a closed-loop control method are proposed as the opening law of the above valve, and the hydraulic motor speed, the pressure at the accumulator inlet and the generated power are chosen as indicators to examine the regulation performance. Then, the synergic effect of the flow control valve and the accumulator in the transient process is discussed. The effectiveness of the two presented control methods on the fluctuation suppression is respectively tested and compared in both regular wave and irregular wave situations via simulation. To validate the practical effectiveness of the proposed methods, field experiments are conducted. The results demonstrate that the open-loop control can only improve the damping ability of the hydraulic PTO in the speed raising stage, while the closed-loop control can improve the stability both in the speed raising stage and in the load increasing stage.

HF-Induced Modifications of the Electron Density Profile in the Earth’s Ionosphere Using the Pump Frequencies near the Fourth Electron Gyroharmonic

We discuss results on plasma density profile modifications in the F-region ionosphere that are caused by HF heating with the frequency f0 in the range [(−150 kHz)–(+75 kHz)] around the fourth electron gyroharmonic 4fc. The experiments were conducted at the HAARP facility in June 2014. A multi-frequency Doppler sounder (MDS), which measures the phase and amplitude of reflected sounding radio waves, complemented by the observations of the stimulated electromagnetic emission (SEE) were used for the diagnostics of the plasma perturbations. We detected noticeable plasma expulsion from the reflection region of the pumping wave and from the upper hybrid region, where the expulsion from the latter was strongly suppressed for f0 ≈ 4fc. The plasma expulsion from the upper hybrid region was accompanied by the sounding wave’s anomalous absorption (AA) slower development for f0 ≈ 4fc. Furthermore, slower development and weaker expulsion were detected for the height region between the pump wave reflection and upper hybrid altitudes. The combined MDS and SEE allowed for establishing an interconnection between different manifestations of the HF-induced ionospheric turbulence and determining the altitude of the most effective pump wave energy input to ionospheric plasma by using the dependence on the offset between f0 and 4fc.

An M Dwarf’s Chromosphere, Corona, and Wind Connection via Nonlinear Alfvén Waves

Abstract An M dwarf’s atmosphere is expected to be highly magnetized. The magnetic energy can be responsible for heating the stellar chromosphere and corona and driving the stellar wind. The nonlinear propagation of Alfvén waves is a promising mechanism for both heating the stellar atmosphere and driving the stellar wind. Based on this Alfvén wave scenario, we carried out a 1D compressive magnetohydrodynamic simulation to reproduce the stellar atmospheres and winds of TRAPPIST-1, Proxima Centauri, YZ CMi, AD Leo, AX Mic, and the Sun. The nonlinear propagation of Alfvén waves from the stellar photosphere to the chromosphere, corona, and interplanetary space is directly resolved in our study. The simulation result particularly shows that the slow shock generated through the nonlinear mode coupling of Alfvén waves is crucially involved in both the dynamics of the stellar chromosphere (stellar spicule) and stellar wind acceleration. Our parameter survey further revealed the following general trends of the physical quantities of the stellar atmosphere and wind. (1) The M dwarf coronae tend to be cooler and denser than the solar corona. (2) The M dwarf stellar winds can be characterized by a relatively faster velocity and much smaller mass-loss rate compared to those of the solar wind. The physical mechanisms behind these tendencies are clarified in this paper, where the stronger stratification of the M dwarf’s atmosphere and relatively smaller Alfvén wave energy input from the M dwarf’s photosphere are remarkable.

The Role of Thermal Denudation in Erosion of Ice-Rich Permafrost Coasts in an Enclosed Bay (Gulf of Kruzenstern, Western Yamal, Russia)

Coastal erosion in the Arctic has numerous internal and external environmental drivers. Internal drivers include sediment composition, permafrost properties and exposure which contribute to its spatial variability, while changing hydrometeorological conditions act as external drivers and determine the temporal evolution of shoreline retreat. To reveal the relative role of these factors, we investigated patterns of coastal dynamics in an enclosed bay in the southwestern Kara Sea, Russia, namely the Gulf of Kruzenstern, which is protected from open-sea waves by the Sharapovy Koshki Islands. Using multitemporal satellite imagery, we calculated decadal-scale retreat rates for erosional segments of the coastal plain from 1964 to 2019. In the field, we studied and described Quaternary sediments and massive ground-ice beds outcropping in the coastal bluffs. Using data from regional hydrometeorological stations and climate reanalysis (ERA), we estimated changes in the air thawing index, sea ice-free period duration, wind-wave energy and total hydrometeorological stress for the Gulf of Kruzenstern, and compared it to Kharasavey and Marre-Sale open-sea segments north and south of the gulf to understand how the hydrometeorological forcing changes in an enclosed bay. The calculated average shoreline retreat rates along the Gulf in 1964–2010 were 0.5 ± 0.2 m yr−1; the highest erosion of up to 1.7 ± 0.2 m yr−1 was typical for segments containing outcrops of massive ground-ice beds and facing to the northwest. These retreat rates, driven by intensive thermal denudation, are comparable to long-term rates measured along open-sea sites known from literature. As a result of recent air temperature and sea ice-free period increases, average erosion rates rose to 0.9 ± 0.7 m yr−1 in 2010–2019, with extremes of up to 2.4 ± 0.7 m yr−1. The increased mean decadal-scale erosion rates were also associated with higher spatial variability in erosion patterns. Analysis of the air thawing index, wave energy potential and their total effect showed that inside the Gulf of Kruzenstern, 85% of coastal erosion is attributable to thermal denudation associated with the air thawing index, if we suppose that at open-sea locations, the input of wave energy and air thawing index is equal. Our findings highlight the importance of permafrost degradation and thermal denudation on increases in ice-rich permafrost bluff erosion in the Arctic.

Flexibility of foundation increases the base shear and horizontal strains during an out–of–plane response to an SH pulse in linear and nonlinear soil

A two-dimensional model of a building supported by a rectangular, flexible foundation embedded in the soil is analysed for excitation by an incident SH-wave pulse. The building and foundation are assumed to be linear while the soil can experience nonlinear deformations. Work expanded on the development of nonlinear strains in the soil can consume a considerable part of the input wave energy, thus leaving less energy for excitation of the building. The soil and foundation are assumed to be isotropic, but the building is taken as anisotropic—it is stiffer in the horizontal direction than in the vertical. The system response with a small nonlinearity in the soil does not differ significantly from the linear response. However, significant differences appear in the responses of the models when a large nonlinearity occurs in the soil. Traditional methods for calculation of the base shear in the design of buildings underestimate the amplitudes and shears that accompany the response of buildings on flexible foundations. Most significant are the large, horizontal strains in the buildings’ foundations and base that result from flexible foundations and from non-vertical incidence of seismic waves.

Resonant wave energy harvester based on dielectric elastomer generator

Dielectric elastomer generators (DEGs) are a class of capacitive solid-state devices that employ highly stretchable dielectrics and conductors to convert mechanical energy into high-voltage direct-current electricity. Their promising performance in terms of convertible energy and power density has been mostly proven in quasi-static experimental tests with prescribed deformation. However, the assessment of their ability in harvesting energy from a dynamic oscillating source of mechanical energy is crucial to demonstrate their effectiveness in practical applications. This paper reports a first demonstration of a DEG system that is able to convert the oscillating energy carried by water waves into electricity. A DEG prototype is built using a commercial polyacrylate film (VHB 4905 by 3M) and an experimental campaign is conducted in a wave-flume facility, i.e. an artificial basin that makes it possible to generate programmed small-scale waves at different frequencies and amplitudes. In resonant conditions, the designed system demonstrates the delivery of a maximum of 0.87 W of electrical power output and 0.64 J energy generated per cycle, with corresponding densities per unit mass of dielectric elastomer of 197 W kg−1 and 145 J kg−1. Additionally, a notable maximum fraction of 18% of the input wave energy is converted into electricity. The presented results provide a promising demonstration of the operation and effectiveness of ocean wave energy converters based on elastic capacitive generators.

Comparison of Different Models for Wave Generation of The Hasselmann Equation

We compare two recently developed sets of source terms, based on different assumptions of wave energy input and dissipation, for Hasselmann equation. The numerical simulation, performed for limited fetch conditions with the constant wind speed shows the difference in total energy and mean frequency distributions along the fetch as well as in wave energy spectra. Possible reasons of such deviations are offered.

Numerical modeling of wave development under the action of wind

Three-dimensional numerical modeling is performed for development of surface waves under the action of wind. The model is based on equations for potential motion of a fluid with a free surface, which are transformed to a curvilinear system of coordinates where the height is counted from the moving surface. The problem is solved in the doubly periodic domain by the Fourier method with calculation of nonlinearity using a high-resolution mesh (Fourier transform method). The three-dimensional elliptic equation for the velocity potential is solved as the Poisson equation by the marching method with iterations. The energy input from wind and the wave energy dissipation are introduced on the basis of the earlier developed and verified algorithms. The long-period evolution of the three-dimensional flow is demonstrated with the wave surface spectra and energy input and output spectra. The results are compared to the experimental data.

Two-dimensional translation, rocking, and waves in a building during soil-structure interaction excited by a plane earthquake P-wave pulse

A two-dimensional model of a building supported by a rectangular, flexible foundation embedded in the soil is analyzed for excitation by an incident plane P-wave. The building, the foundation, and the soil have different material properties. The building is assumed to be anisotropic and linear, while the soil and the foundation are assumed to be isotropic and can experience nonlinear deformations. In general, the work spent for the development of nonlinear strains in the soil can consume a significant part of the input wave energy and thus less energy is available for the excitation of the building. However, in the case of excitation by a plane P-wave pulse, we show that the nonlinear response in the soil and the foundation does not significantly change the nature of excitation in the base of the building. It is noted that the response of a building can be approximated by base translation and rocking for excitation by long, strong motion waves.

Two-dimensional translation, rocking, and waves in a building during soil-structure interaction excited by a plane earthquake SV-wave pulse

A two-dimensional (2-D) model of a building supported by a rectangular, flexible foundation embedded in the soil is analyzed for excitation by an incident plane SV-wave. The incidence is below the critical angle. The building is assumed to be anisotropic and linear while the soil and the foundation are assumed to be isotropic and can experience nonlinear deformations. In general the work spent for the development of nonlinear strains in the soil can consume a significant part of the input wave energy and thus less energy is available for the excitation of the building. We show that the energy distribution in the building depends on the nature of the incident wave and differs substantially between the cases of incident P- and SV-waves. However, for both excitation by a plane SV-wave pulse and excitation by a P-wave, we show that the nonlinear response in the soil and the foundation does not significantly change the nature of excitation of the base of the building. It is noted that the building response can be approximated by translation and rocking of the base only for excitation by long, strong motion waves.

The “Alfvénic surge” at substorm onset/expansion and the formation of “Inverted Vs”: Cluster and IMAGE observations

AbstractFrom multipoint, in situ observations and imaging, we reveal the injection‐powered, Alfvénic nature of auroral acceleration during onset and expansion of a substorm. It is shown how Alfvénic variations over time dissipate to form large‐scale, inverted‐V structures characteristic of quasistatic aurora. This characterization is made possible through the fortuitous occurrence of a substorm onset and expansion phase on field lines traversed by Cluster in the high‐altitude acceleration region. Substorm onset was preceded by the occurrence of multiple poleward boundary intensifications (PBIs) and subsequent development/progression of a streamer toward the growth phase arc indicating that this is of the PBI‐/streamer‐triggered class of substorms. Onset on Cluster is marked by the injection of hot, dense magnetospheric plasma in a region tied to one of the preexisting PBI current systems. This was accompanied by a surge of Alfvénic activity and enhanced inverted‐V acceleration, as the PBI current system intensified and striated to dispersive scale Alfvén waves. The growth of Alfvén wave activity was significant (up to a factor of 300 increase in magnetic field power spectral density at frequencies 20 mHz few hertz) and coincided with moderate growth (factor 3–5) in the background PBI current. This sequence is indicative of a cascade process whereby small‐scale/dispersive Alfvén waves are generated from large‐scale Alfvén waves or current destabilization. It also demonstrates that the initial PBIs and their subsequent evolution are an intrinsic part of the global auroral substorm response to injection and accompanying wave energy input from the magnetotail. Alfvénic activity persisted poleward of the PBI currents composing a broad Alfvén wave‐dominated region extending to the polar cap edge. These waves have transverse scales ranging from a few tens of kilometers to below the ion gyroradius and are associated with large electric fields (up to 200 mV/m) and Poynting fluxes (up to 200 mW/m2 mapped at ionospheric altitudes). The fluctuations show mixtures of traveling and/or reflected (including standing) wave signatures, depending on frequency and location. A transition from incoming traveling wave to standing wave signatures is also seen near onset. Depending on location, electron distributions show signatures of Alfvén acceleration, inverted‐V acceleration, or evidence of both. Poleward expansion of substorm emissions coincided with the poleward expansion of the hot energetic plasma, and the formation of a large‐scale inverted‐V current system with concurrent attenuation of Alfvénic fluctuations within the Alfvén‐dominated region. We suggest that the attenuation is due to a dissipative effect owing to changes in the dispersive properties of these waves via the injection process and/or due to a transient magnetotail source. These findings suggest that in addition to playing active roles in driving substorm aurora, inverted‐V and Alfvénic acceleration processes are causally linked.

Translation, torsion, and wave excitation of a building during soil–structure interaction excited by an earthquake SH pulse

A two-dimensional (2-D) model of a building supported by a rectangular, flexible foundation embedded in the soil is analyzed. The building, the foundation, and the soil have different physical properties. The building is assumed to be linear, but the soil and the foundation can experience nonlinear deformations. While the work spent for the development of nonlinear strains in the soil can consume a significant part of the input wave energy—and thus less energy is available for the excitation of the building—the nonlinear response in the soil and the foundation does not signficantly alter the nature of excitation of the base of the building. It is noted that the response of a building can be approximated by translation and torsion of the base for excitation by long, strong motion waves.

Simulation of one-dimensional evolution of wind waves in a deep water

A direct wave model based on the one-dimensional nonlinear equations for potential waves is used for simulation of wave field development under the action of energy input, dissipation, and nonlinear wave-wave interaction. The equations are written in conformal surface-fitted nonstationary coordinate system. New schemes for calculating the input and dissipation of wave energy are implemented. The wind input is calculated on the basis of the parameterization developed through the coupled modeling of waves and turbulent boundary layer. The wave dissipation algorithm, introduced to prevent wave breaking instability, is based on highly selective smoothing of the wave surface and surface potential. The integration is performed in Fourier domain with the number of modes M = 2048, broad enough to reproduce the energy downshifting. As the initial conditions, the wave field is assigned as train of Stokes waves with steepness ak = 0.15 at nondimensional wavenumber k = 512. Under the action of nonlinearity and energy input the spectrum starts to grow. This growth is followed by the downshifting. The total time of integration is equal to 7203 initial wave periods. During this time the energy increased by 1111 times. Peak of the spectrum gradually shifts from wavenumber nondimensional k = 512 down to k = 10. Significant wave height increases 33 times, while the peak period increases 51 times. Rates of the peak downshift and wave energy evolution are in good agreement with the JONSWAP formulation.

Sensitivity of the Ocean State to Lee Wave–Driven Mixing

Abstract Diapycnal mixing plays a key role in maintaining the ocean stratification and the meridional overturning circulation (MOC). In the ocean interior, it is mainly sustained by breaking internal waves. Two important classes of internal waves are internal tides and lee waves, generated by barotropic tides and geostrophic flows interacting with rough topography, respectively. Currently, regarding internal wave–driven mixing, most climate models only explicitly parameterize the local dissipation of internal tides. In this study, the authors explore the combined effects of internal tide– and lee wave–driven mixing on the ocean state. A series of sensitivity experiments using the Geophysical Fluid Dynamics Laboratory CM2G ocean–ice–atmosphere coupled model are performed, including a parameterization of lee wave–driven mixing using a recent estimate for the global map of energy conversion into lee waves, in addition to the tidal mixing parameterization. It is shown that, although the global energy input in the deep ocean into lee waves (0.2 TW; where 1 TW = 1012 W) is small compared to that into internal tides (1.4 TW), lee wave–driven mixing makes a significant impact on the ocean state, notably on the ocean thermal structure and stratification, as well as on the MOC. The vertically integrated circulation is also impacted in the Southern Ocean, which accounts for half of the lee wave energy flux. Finally, it is shown that the different spatial distribution of the internal tide and lee wave energy input impacts the sensitivity described in this study. These results suggest that lee wave–driven mixing should be parameterized in climate models, preferably using more physically based parameterizations that allow the internal lee wave–driven mixing to evolve in a changing ocean.