Total Wave Energy Research Articles

Wave energy evolution and vortex dynamics induced by gap resonance between multiple floating rectangular structures

This study presents an experimental design and implementation aimed at investigating the processes of wave energy evolution and vortex generation and shedding under wave-induced gap resonance between multiple floating rectangular structures (MFRSs). A synchronized particle image velocimetry system, combined with an efficient data processing method, is adopted to study the wave energy evolution from the initial to the quasi-steady state. The validity of experiment was confirmed by published experimental and numerical data, regarding variations of resonant wave height vs dimensionless incident wave numbers and free surface elevations. The intrinsic nature of two distinct gap resonant frequencies was clarified through comprehensive analyses of the flow field and phase difference of the free surface elevation. The resonant characteristics, total wave energy dissipation, and the contributions of viscous dissipation from wall friction and flow separation around two gaps of MFRSs were estimated quantitatively. The Ω-criterion vortex identification method was selected to investigate vortex generation, shedding, and dissipation modes of MFRSs. The results indicate that the second resonant frequency in gap 1 is primarily induced by fluid motion oscillations in gap 2. A substantial portion of the incident wave energy, approximately 55.4%, is dissipated under gap resonance. The diameter of vortex structures at the fundamental resonant wave frequency in gap 1 is at least three times larger than that at the second resonant wave frequency. The energy accumulated by the water blockage effect of vortex structures significantly exceeds the energy dissipated by the increased vortex generation and shedding under wave-induced gap resonance.

Experimental Investigation on Wave and Bed Profile Evolution in a Sandbar-Lagoon Coast with Submerged Vegetation

Better understanding of the hydro- and morphodynamic processes within vegetated sandbar-lagoon coasts is important for assessing the coastal protection capability of vegetation meadow for the coastal environments. Eighteen flume tests were conducted in a mobile-bed sandbar-lagoon with mimicked submerged vegetation under different water depths and wave conditions. It was found that wave attenuation by submerged vegetation near the breaking point is significant. An empirical linear expression for the total wave energy change ratio is proposed with a determination coefficient of 0.84. Moreover, the quantitative formulae for the erosion volume and maximum erosion thickness of sandbars and foredunes, as well as the total sediment transport volume, were proposed to demonstrate the implications of submerged vegetation meadows. These findings provide scientific references for coastal management and conservation planning, especially for sandbar-lagoon coasts. Nevertheless, additional physical experiments or field data are necessary to further validate those formulae.

Wave turbulence in a rotating channel: numerical implementation and results

The analysis of Scott (J. Fluid Mech., vol. 741, 2014, pp. 316–349) is implemented numerically. Decaying turbulence is confined to a channel between two infinite, parallel, rotating walls. The Rossby and Ekman numbers are supposed small, the former condition making nonlinearity small, while the latter allows the turbulence to persist for the many rotational periods needed for the small nonlinearity to be effective. The flow is expressed as a combination of inertial waveguide modes, indexed by a two-dimensional wave vector $\boldsymbol{k}$ and an integer n. The $n = 0$ modes form a two-dimensional component of the flow, whereas the remainder is the wave component, on which attention is focused in this article. Assuming statistical axisymmetry and homogeneity in directions parallel to the walls, the second-order moments of the mode amplitudes yield a spectral matrix ${A_{nm}}(k,t)$ (where $k = |\boldsymbol{k} |$ ), of which the diagonal elements describe the distribution of energy over different modes. Wave-turbulence analysis provides an equation governing the time evolution of ${A_{nn}}$ , $n \ne 0$ , the wave spectra, which forms the basis for the present work. The initial distribution of energy is Gaussian and depends on a parameter $\varXi$ , the initial spectral width. The problem has two other parameters, ${\beta _w}$ and ${\beta _v}$ , which correspond to two distinct viscous dissipative mechanisms: wall damping due to boundary layers and volumetric damping by viscous effects throughout the flow. Results obtained by numerical solution include the time evolution of the total wave energy, E, and the detailed description of its distribution over k and n provided by ${A_{nn}}(k)$ .

Utility of ocean wave parameters in ambient noise predictiona).

This study is concerned with prediction of the "wind noise" component of ambient noise (AN) in the ocean. It builds on the seminal paper by Felizardo and Melville [(1995). J. Phys. Oceanogr. 25, 513-532], in which the authors quantified the correlation between AN and individual wind/wave parameters. Acoustic data are obtained from hydrophones at six diverse locations, and wind/wave parameters are obtained from moored buoys and numerical models. We describe a procedure developed for this study that identifies correlation of AN with wave parameters, independent of their mutual correlation with wind speed. We then describe paired calibration/prediction experiments, whereby multiple wind/wave parameters are used simultaneously to estimate AN. We find that the improvement from inclusion of wave parameters is robust but marginal; typically, root mean square error (RMSE) is reduced by less than 0.3 dB and/or less than 12% of the original RMSE. We interpret the latter outcome as suggesting that wave breaking responds to changes in local winds quickly, relative to, for example, total wave energy, which develops more slowly. This outcome is consistent with prior observations of wave breaking, e.g., Babanin [(2011). Breaking and Dissipation of Ocean Surface Waves (Cambridge University Press, Cambridge, UK), Chap. 3]. We discuss this in context of the time/space response of various wave parameters to wind forcing.

Floating wave energy farms: How energy calculations shape economic feasibility?

The aim of this study is to use two different methodologies for calculating the energy produced by a total wave energy farm in the Cantabrian Sea (North of Spain). First method studies the energy produced by the farm taking into account the wave energy converter power matrix and the probability matrix of sea conditions for a particular location. On the other hand, second method is a more simplified methodology in which the wave energy converter power matrix is not taken into account, but it considers the density of the water, gravity, period and height of the wave, as well as the percentage of efficiency, among others. Finally, the energy generated by the farm and the economic parameters that allow calculating its economic feasibility are studied, such as Levelized Cost of Energy, Net Present Value and Internal Rate of Return. Results indicate the importance of using a particular method for calculating the energy produced by a wave energy farm in terms of the variation of its economic feasibility. In this sense, it is shown that despite the fact that the first method is more detailed, the variations between both methods are very small, therefore the simplest model can be used in the future studies, reducing the calculation process in the future.

Effect of area divergence and frequency on damping of slow magnetoacoustic waves propagating along umbral fan loops

ABSTRACT Waves play an important role in the heating of solar atmosphere; however, observations of wave propagation and damping from the solar photosphere to corona through chromosphere and transition region are very rare. Recent observations have shown propagation of 3-min slow magnetoacoustic waves (SMAWs) along fan loops from the solar photosphere to corona. In this work, we investigate the role of area divergence and frequencies on the damping of SMAWs propagating from the photosphere to the corona along several fan loops rooted in the sunspot umbra. We study the Fourier power spectra of oscillations along fan loops at each atmospheric height which showed significant enhancements in 1–2, 2.3–3.6, and 4.2–6 min period bands. Amplitude of intensity oscillations in different period bands and heights are extracted after normalizing the filtered light curves with low-frequency background. We find damping of SMAW energy flux propagating along the fan loop 6 with damping lengths $\approx 170$ and $\approx 208$ km for 1.5- and 3-min period bands. We also show the decay of total wave energy content with height after incorporating area divergence effect, and present actual damping of SMAWs from photosphere to corona. Actual damping lengths in this case increases to $\approx 172$ and $\approx 303$ km for 1.5- and 3-min period bands. All the fan loops show such increase in actual damping lengths, and thus highlight the importance of area divergence effect. Results also show some frequency-dependent damping of SMAW energy fluxes with height where high-frequency waves are damped faster than low-frequency waves.

Sausage, kink, and fluting magnetohydrodynamic wave modes identified in solar magnetic pores by Solar Orbiter/PHI

Solar pores are intense concentrations of magnetic flux that emerge through the solar photosphere. When compared to sunspots, they are much smaller in diameter and can therefore be affected and buffeted by neighbouring granular activity to generate significant magnetohydrodynamic (MHD) wave energy flux within their confines. However, observations of solar pores from ground-based telescope facilities may struggle to capture subtle motions that are synonymous with higher-order MHD wave signatures because of the seeing effects that are produced in the Earth’s atmosphere. Hence, we exploited timely seeing-free and high-quality observations of four small magnetic pores from the High Resolution Telescope (HRT) of the Polarimetric and Helioseismic Imager (PHI) on board the Solar Orbiter spacecraft during its first close perihelion passage in March 2022 (at a distance of 0.5 au from the Sun). Through acquisition of data under stable observing conditions, we were able to measure the area fluctuations and horizontal displacements of the solar pores. Cross correlations between perturbations in intensity, area, line-of-sight velocity, and magnetic fields, coupled with the first-time application of novel proper orthogonal decomposition techniques on the boundary oscillations, provided a comprehensive diagnosis of the embedded MHD waves as sausage and kink modes. Additionally, the previously elusive m = 2 fluting mode is identified in the most magnetically isolated of the four pores. An important consideration lies in how the identified wave modes contribute to the transfer of energy into the upper solar atmosphere. Approximately 56%, 72%, 52%, and 34% of the total wave energy of the four pores we examined is associated with the identified sausage modes and about 23%, 17%, 39%, and 49% with their kink modes, while the first pore also receives a contribution of about 11% linked to the fluting mode. This study reports the first-time identification of concurrent sausage, kink, and fluting MHD wave modes in solar magnetic pores.

Relative energy and perceived impact of vessel-generated waves in fetch-limited environments

Houser C, Carswell A, Chittle B, Johnson G, Caschera A, Smith A. 2024. Relative energy and perceived impact of vessel-generated waves in fetch-limited environments. Lake Reserv Manag. 40:285–302 Vessel-generated waves (or wakes) are perceived as an important stressor in both marine and freshwater systems, and they are an increasingly important focus of coastal management. Recent studies suggest that wakes account for a significant portion of the total wave energy in fetch-limited environments and in turn have the potential to resuspend sediment, erode shorelines, degrade water quality, damage infrastructure, and disrupt aquatic ecosystems, in addition to being considered a safety hazard and a nuisance. To assess the relative contribution of wakes to the total wave energy, monitoring was completed at 32 sites across 7 fetch-limited lakes in Ontario, Canada between 2020 and 2023. The percent wake energy was inversely related to the average fetch length, with deviations to the relationship dependent on whether the site was open, an embayment or along a narrow section of the lake. A survey of property owners and residents suggests that the perceived impact of wakes also varies with the fetch length. Shoreline erosion and degraded water quality were identified as primary impacts of wakes in lakes with the smallest average fetch, but very few respondents provided direct evidence of boat wake impacts. Most respondents described vessel operation, experience of the vessel operator and conflict over different boating uses as the primary issues associated with wakes. While boat wakes may contribute a significant portion of the wave energy in fetch-limited lakes, further research is required to determine when and where they may represent a physical and ecological stressor rather than being just a nuisance.

Wave attenuation and transformation across a highly turbid muddy tidal flat-salt marsh system

Understanding wave processes within the coastal system is crucial for the appropriate design of coastal prevention engineering and offshore structures. To address the limitations of field observations and traditional methods, an array of pressure sensors and optical instruments were deployed across a shoreward intertidal flat consisting of the fluid muddy seabed, bare flat, and salt marsh in a highly turbid coastal area. We found that the Spartina alterniflora salt marsh has the strongest wave dissipation capacity. Although bare flats have the weakest wave dissipation capacity, they are the most extensive within the intertidal zone, resulting in substantial total wave energy dissipation. A noteworthy positive feedback between fluid mud and wave dissipation is observed. Additionally, the incident waves undergo complex transitions during propagation, which are strongly modulated by tidal influences. In particular, when the wave propagation direction is opposite to the tidal current, there is an amplification of wave energy within the tidal flat. This amplification is attributed to the "jacking effect" of the tidal current, hindering the transformation of the wind waves into the low-energy capillary waves. It is important to note that the high-energy infragravity waves are gradually released and steadily increase as the incident waves propagate shoreward. This implies their potentially significant role in nearshore processes, especially during extreme dynamic events or along extensive coastlines.

A simple image correlation technique for imaging subsurface damage from low-velocity impacts in composite structures

A robust computer vision system is proposed to visualize subsurface barely visible impact damage (BVID) in composite structures through a simple image correlation technique together with a damage imaging condition. This system uses a digital camera to record a video of the surface motion, capturing micron-scale dynamic movement from guided waves propagating on the surface of the structure generated via a sweeping frequency excitation (chirp) up to the ultrasonic frequency range. As the excitation frequency changes during the chirp, waves become trapped within this damaged region, forming standing waves to generate local resonance at specific frequencies. This localized resonance accumulates high wave energy in the region, generating a higher transverse displacement at the damage site compared to the remaining part of the structure. In this work, a simple image correlation technique is proposed to correlate each filtered video frame with the temporal mean of the filtered wavefield video to highlight standing waves at localized damage. The proposed image correlation technique is distinct from digital image correlation (DIC) since it does not use correlation for subset matching to track the movement of surface patterns between two images (video frames). Instead, it uses correlation to directly quantify similarities between corresponding image pixels (windows). Utilizing a single camera greatly simplifies system complexity and hence enhances the practicality and potential for real-time performance over a recently developed technique that utilized 3D DIC with a stereo camera for vision-based BVID detection. To realize the aim, work was conducted in two sequential steps: (1) off-axis 2D DIC was employed rather than 3D DIC to examine the potential of employing a single camera to capture images and extract not only in-plane displacement but also a fraction of transverse displacement in which local resonance is dominant and (2) image correlation was then employed, supplanting the off-axis 2D DIC image processing involved in the first step, to highlight the damage with significantly less processing complexity. This proposed technique using a zero-mean normalized cross-correlation imaging condition, rather than the total wave energy used for DIC-based approaches, is efficient and effective for identifying regions of minute surface movement from local resonance within the damage region without the use of the computationally intensive interpolation to get the sub-pixel gray level information followed by subset matching employed in DIC-based image processing. Two geometrically identical CFRP composite honeycomb panels that had been subjected to low-velocity impacts were used for verification and validation, and two excitation location configurations were tested for each panel. Damaged images produced with correlation for a 100 mm × 100 mm field of view using a single 3-s video, or a total of 19,200 video frames, show accurate damage imaging capabilities regardless of excitation location that exceed that of DIC techniques and is comparable to benchmark damage images obtained from laser Doppler vibrometry, ultrasonic C-scans, and X-ray CT scans. This success of correlation-based imaging of subsurface BVID demonstrates substantial improvements in efficiency and practicality and shows high potential for in situ and real-time computer vision-based nondestructive inspection or structural health monitoring of subsurface BVID in composite aircraft and other critical structures.

Sum-frequency triad interactions among surface waves propagating through an ice sheet

We study nonlinear resonant wave–wave interactions which occur when ocean waves propagate into a thin floating ice sheet. Using multiple-scale perturbation analysis, we obtain theoretical predictions of the wave amplitude evolution as a function of distance travelled past the ice edge for a semi-infinite ice sheet. The theoretical predictions are supported by a high-order spectral (HOS) method capable of simulating nonlinear interactions in both open water and the ice sheet. Using the HOS method, the amplitude evolution predictions are extended to multiple (coupled) triad interactions and a single ice sheet of finite length. We relate the amplitude evolution to mechanisms with strong frequency dependence – ice bending strain, related to ice breakup, as well as wave reflection and transmission. We show that, due to sum-frequency interactions, the maximum strain in the ice sheet can be more than twice that predicted by linearised theory. For an ice sheet of finite length, we show that nonlinear wave reflection and transmission coefficients depend on a parameter in terms of wave steepness and ice length, and can have values significantly different than those from linear theory. In particular, we show that nonlinear sum-frequency interactions can appreciably decrease the total wave energy transmitted past the ice sheet. This work has implications for understanding the occurrence of ice breakup, wave attenuation due to scattering in the marginal ice zone and the resulting ice floe size distribution.

Relativistic Schrödinger equation and probability currents for free particles

In this work, we start from the problem of quantizing the relativistic Hamiltonian of a free massive particle (rest mass different from 0), a problem exceptionally difficult in the standard approaches to quantum mechanics. In fact, in tempered distribution state space, we find the natural way to define the relativistic Hamiltonian operator and its associated Schrödinger equation The existence of a linear continuous Hermitian operator associated with the Einstein's Hamiltonian of a free particle, defined on the entire tempered distribution space, automatically implies the conservation of Born probability flux (which doesn't mean the conservation of particles number, rather it implies the conservation of the total relativistic energy of the solution wave). We, then, deduce the continuity equation for the Born probability density and study some its different (but equivalent) expressions. We determine some possible forms of probability currents and flux velocity fields associated with the particle evolution. We provide the relativistic invariant expression for both Schrödinger equation and probability flux continuity equations.

Multi-Sensor Observations Reveal Large-Amplitude Nonlinear Internal Waves in the Kara Gates, Arctic Ocean

We present multi-sensor measurements from satellites, unmanned aerial vehicle, marine radar, thermal profilers, and repeated conductivity–temperature–depth casts made in the Kara Gates strait connecting the Barents and the Kara Seas during spring tide in August 2021. Analysis of the field data during an 18-h period from four stations provides evidence that a complex sill in the Kara Gates is the site of regular production of intense large-amplitude nonlinear internal waves. Satellite data show a presence of a relatively warm northeastward surface current from the Barents Sea toward the Kara Sea attaining 0.8–0.9 m/s. Triangle-shaped measurements using three thermal profilers revealed pronounced vertical thermocline oscillations up to 40 m associated with propagation of short-period nonlinear internal waves of depression generated by stratified flow passing a system of shallow sills in the strait. The most intense waves were recorded during the ebb tide slackening and reversal when the background flow was predominantly supercritical. Observed internal waves had wavelengths of ~100 m and traveled northeastward with phase speeds of 0.8–0.9 m/s. The total internal wave energy per unit crest length for the largest waves was estimated to be equal to 1.0–1.8 MJ/m.

Optimal Smoothing of the Wind–Wave Spectrum Based on the Confidence-Interval Trade-Off

In this study, a smoothing method was applied to improve the accuracy of peak wave period estimation using water surface elevation data collected from two oceanographic and meteorological observation towers situated on the western coast of the Korean Peninsula. The effectiveness of the smoothing method was validated by assessing the surface elevation variance and total wave energy. Subsequently, we examined the impact of the smoothing application. The results of our analysis revealed a reduction of approximately 27% in comparison to the confidence interval of the initially estimated spectrum upon applying the smoothing method. Furthermore, a slight variation of approximately 1–2 s was observed between the peak wave period calculated from the estimated spectrum and that obtained through the smoothing process. Utilizing statistical methods to determine the optimal smoothing parameter count, we observed an increasing trend as the range of significant wave heights decreased.

Utility of ocean wave parameters for improving predictions of ambient noise

This study is concerned with prediction of the “wind noise” component of ambient noise (AN) in the ocean. It builds on the seminal paper by Felizardo and Melville (1995), in which the authors quantified the correlation between AN and individual wind/wave parameters. We utilize hydrophone observations deployed in the north and northeast Pacific Ocean. Wind/wave parameters are obtained from moored buoys and numerical models. We describe a procedure developed for this study which isolates the correlation of AN with wave parameters, independent of mutual correlation with wind speed (residual correlation). We then describe paired calibration/prediction experiments, whereby multiple wind/wave parameters are used simultaneously to estimate AN. We find that the improvement from inclusion of wave parameters is robust but modest. We interpret the latter outcome as suggesting that wave breaking responds to changes in local winds quickly, relative to, for example, total wave energy, which develops more slowly. This outcome is consistent with prior knowledge of the physics of wave breaking, e.g., Babanin (2011). We discuss this in context of the wave spectrum's time/space response to wind forcing.

An approach to assess the potential of wave energy resources based on directional energy flux

Estimating the total available wave energy surrounding islands holds significant importance in accessing the hosting capacity of wave energy. This study proposes a novel method for estimating the total available wave energy resources around islands using directional wave energy flux as a key parameter. By introducing the concept of directional across section, this method incorporates the directionality into the total resource calculation. A case study of the northern Zhoushan Archipelago was conducted to demonstrate the practical application of this method. The wave conditions were computed using the SWAN wave model for a 10-year period and validated against 7 months of buoy observations near Shengshan island. Basic wave energy resource characteristics were analyzed and the spatiotemporal features were analyzed using various indices. Subsequently, the proposed method was applied to calculated the total available wave energy around islands at various extend distances from the coastline. The wave energy potential of the islands in the study area stands at 349 MW, 302 MW, 318 MW, and 387 MW respectively, at extend distances of 5 km, 7.5 km, 10 km, and 12.5 km from the shoreline. These values represent approximately 25.1%–42.2% of the total energy obtained using existing methods.

Propagation of Dirac waves through various temporal interfaces, slabs, and crystals

We investigate the influence of the temporal variations of various medium parameters on the propagation of Dirac-type waves in materials where the quasiparticles are described by a generalized version of the pseudospin-1/2 Dirac equation. Our considerations also include the propagation of electromagnetic waves in metamaterials with the Dirac-type dispersion. We focus on the variations of the scalar and vector potentials, mass, Fermi velocity, and tilt velocity describing the Dirac cone tilt. We derive the scattering coefficients associated with the temporal interfaces and slabs analytically and find that the temporal scattering is caused by the changes of the mass, Fermi velocity, and vector potential, but does not arise from the changes of the scalar potential and tilt velocity. We also explore the conditions under which the temporal Brewster effect and total interband transition occur and calculate the change in total wave energy. We examine bilayer Dirac temporal crystals where parameters switch between two different sets of values periodically and prove that these systems do not have momentum gaps. Finally, we assess the potential for observing these temporal scattering effects in experiments.

Subsurface impact damage imaging for composite structures using 3D digital image correlation

An integrated system is proposed to visualize subsurface barely visible impact damage (BVID) in composite structures using three-dimensional (3D) digital image correlation (3D DIC). This system uses a pair of digital cameras to record video frames in the field-of-view (FOV) of the structure’s surface, capturing the wavefield generated via chirp excitation in the near-ultrasonic frequency range. Significant pitfalls of previous efforts of damage imaging using two-dimensional DIC have been largely mitigated. First, 3D DIC enables capturing out-of-plane displacements, which are much larger in amplitude versus in-plane displacements that a single camera would be limited to sensing, thus increasing the signal-to-noise ratio. This enhancement in turn increases the sensitivity of the stereo-camera system. Second, a total wave energy (TWE) damage imaging condition is proposed to visualize the local damage region. The monogenic signal obtained via Reisz transform (RT) is employed to compute the instantaneous amplitude, with which the local wave energy can be calculated spatially over time. Since a high displacement amplitude and thus high wave energy will occur in the damage region due to the local resonance, the proposed TWE imaging condition can relax the Nyquist sampling requirement, unlike guided-wave-based structural health monitoring techniques which require fully reconstructing the wavefield and wave modes through sampling that satisfies the Nyquist criterion. As such, a much lower camera frame rate is adequate for the proposed system. Consequently, the maximum spatial resolution of the camera for a given FOV can be achieved at the expense of a reduced frame rate. With the maximized pixel resolution and reduced frame rate for employing the TWE imaging condition, composite structures can be inspected or monitored with a larger FOV. As a result, there is no longer any need to apply signal enhancement techniques, such as sample interleaving, image stitching, or averaging, to increase the effective performance of the camera. Rather than needing thousands of repeated videos for minimizing the incoherent noise, only a single stereo-video with a few seconds of sampling duration is necessary for damage imaging. The use of a powerful piezo-shaker also increases the wave signal amplitude and further enhances sensitivity without permanent adhesion. To demonstrate this stereo-camera concept with the TWE imaging condition, the system was used to image damage in two carbon fiber reinforced polymer composite honeycomb panels, which had been subjected to low-velocity impacts (2 J). For each panel, two excitation configurations were used to verify the robustness of the system. Initial damage maps produced for a 100 × 100-mm FOV using a three-second stereo-video show accurate damage imaging ability that is independent of excitation location and comparable to benchmark damage images computed from laser Doppler vibrometer data and those gathered from ultrasonic and X-ray computerized tomography scans. This efficient and reliable integrated system demonstrated high potential for in-time damage inspection on composite aircraft and other critical structures.

Spatial and temporal wave climate variability along the south coast of Sweden during 1959–2021

This study presents 62 years of hindcast wave climate data for the south coast of Sweden from 1959–2021. The 100-km-long coast consists mainly of sandy beaches and eroding bluffs interrupted by headlands and harbours alongshore, making it sensitive to variations in incoming wave direction. A SWAN wave model of the Baltic Sea, extending from the North Sea to the Åland Sea, was calibrated and validated against wave observations from 16 locations distributed within the model domain. Wave data collected from open databases were complemented with new wave buoy observations from two nearshore locations within the study area at 14 and 15 m depth. The simulated significant wave height showed good agreement with the local observations, with an average R2 of 0.83. The multi-decadal hindcast data was used to analyse spatial and temporal wave climate variability. The results show that the directional distribution of incoming waves varies along the coast, with a gradually increasing wave energy exposure from the west towards the east. The wave climate is most energetic from October to March, with the highest wave heights in November, December, and January. In general, waves from westerly directions dominate the annual wave energy, but within the hindcast time series, a few years had larger wave energy from easterly directions. The interannual variability of total wave energy and wave direction is correlated to the North Atlantic Oscillation (NAO) index. In the offshore, the total annual wave energy had a statistically significant positive correlation with the NAO DJFM station-based index, with a Spearman rank correlation coefficient of 0.51. In the nearshore, the correlation was even stronger. Future studies should investigate the possibility of using the NAO index as a proxy for the wave energy direction and its effect on coastal evolution.

Analytical and numerical investigation on the energy of free and locked tsunami waves generated by a submarine landslide

Submarine landslides are capable of causing locally catastrophic tsunamis. Landslide parameters, particularly those related to the landslide motion, are highly uncertain in a real landslide tsunami event. To date, a practical method for effectively and efficiently modeling the landslide tsunami generation process is still lacking. To gain insight into the landslide tsunami generation mechanism, we employed a combination of analytical derivation and numerical computation. From the wave energy perspective, we found the locked wave component of a landslide tsunami to be as important as the free wave component. Thus, the locked wave component cannot be neglected. We showed that for a geophysically relevant submarine landslide speed, the locked wave component has a deceivingly small wave amplitude with large flow velocities. Thus, careful attention must be paid to flow velocities when modeling landslide tsunamis. For a submarine landslide forcing water waves at a constant speed, we found that the total wave energy first evolves from zero to a peak value, before decreasing to an asymptotic value. These two distinct energy values and the corresponding wave generation times may serve as conservative estimates in predictive studies, in which precise information on the landslide dynamics is impossible to obtain. Finally, we used the 1998 Papua New Guinea landslide tsunami as an example to demonstrate how the findings in this study aid in the modeling effort for a real event.