Surface Wave Spectra Research Articles

Localization of elastic surface waves based on defect modes in non-Bragg structures

Abstract The non-Bragg defect mode (NBDM) of elastic surface waves is experimentally investigated by inserting a defect in the middle of an antisymmetric periodic corrugated aluminum plate, which has been known as the non-Bragg structures since the observed band gaps are different from the traditional Bragg ones. Generally, the non-Bragg band gaps, existing away from the Bragg ones in a perfectly periodic waveguide, are created by the resonances of different transverse guided modes. The transmission spectra of elastic surface waves in antisymmetric structures with defects reveal the presence of defect modes within the non-Bragg gaps. Notably, the NBDM exhibits significant distribution characteristics in comparison to the traditional Bragg defect mode, including more complex elastic wave higher-order modes and localized wave energy near the defect. Consequently, the NBDM observed in the antisymmetric periodic waveguide with defects holds potential for utilization in other elastic wave functional devices, including filters and wave intensifiers.

Large Eddy Simulation of Cross‐Shore Hydrodynamics Under Random Waves in the Inner Surf and Swash Zones

AbstractA 3D large eddy simulation coupled with a free surface tracking scheme was used to simulate cross‐shore hydrodynamics as observed in a large wave flume experiment. The primary objective was to enhance the understanding of wave‐backwash interactions and the implications for observed morphodynamics. Two simulation cases were carried out to elucidate key processes of wave‐backwash interactions across two distinct stages: berm erosion and sandbar formation, during the early portion of a modeled storm. The major difference between the two cases was the bathymetry: one featuring a berm without a sandbar (Case I), and the other, featuring a sandbar without a berm (Case II) at similar water depth. Good agreement (overall Willmott's index of agreement greater than 0.8) between simulations and measured data in free surface elevation, wave spectrum, and flow velocities validated the model skill. The findings indicated that the bottom shear stress, represented by the Shields parameter, was significant in both cases, potentially contributing substantial sediment transport. Notably, the occurrence of intense wave‐backwash interactions were more frequent in the absence of a sandbar. These intense wave‐backwash interactions resulted in a pronounced horizontal pressure gradient, quantified by high Sleath parameters, exceeding the criteria for momentary bed failure. Additionally, a more vigorous turbulence‐bed interaction, characterized by near‐bed turbulent kinetic energy, was observed in the case lacking a sandbar, potentially augmenting sediment suspension. These insights are pivotal in understanding the mechanisms underlying berm erosion and how sandbar formation serves to protect further beach erosion.

In Situ Observations at the Air‐Sea Interface by Expendable Air‐Deployed Drifters Under Hurricane Michael (2018)

AbstractAn array of surface drifters deployed ahead of Hurricane Michael measured the surface temperature, pressure, directional wind and wave spectra, and surface currents one day before it made landfall as a Category 5 Hurricane. The drifters, 25–50 km apart, spanned two counter‐rotating ocean eddies as Hurricane Michael rapidly intensified. The drifters measured the shift of wave energy between frequency bands in each quadrant of the storm, the response of upper ocean currents, and the resulting cold wake following Michael's passage. Wave energy was greatest in the front quadrants and rapidly decreased in the left‐rear quadrant, where wind and wave energy were misaligned, and components of the wave field were aligned with currents. Hurricane Michael's wave field agreed with previous studies of nondirectional wave spectra across multiple tropical cyclones but had some unique characteristics. The analysis demonstrates how co‐located surface wind and wave observations can complement existing airborne and satellite observations.

A method for constructing directional surface wave spectra from ICESat-2 altimetry

Abstract. Sea ice is important for Earth's energy budget as it influences surface albedo and air–sea fluxes in polar regions. On its margins, waves heavily impact sea ice. Routine and repeat observations of waves in sea ice are currently lacking, and therefore a comprehensive understanding of how waves interact with sea ice and are attenuated by it is elusive. In this paper, we develop methods to separate the two-dimensional (2D) surface wave spectra from sea-ice height observations made by the ICESat-2 (IS2) laser altimeter, a polar-orbiting satellite. A combination of a linear inverse method, called generalized Fourier transform (GFT), to estimate the wave spectra along each beam and a Metropolis–Hastings (MH) algorithm to estimate the dominant wave's incident angle was developed. It allows us to estimate the 2D wave signal and its uncertainty from the high-density, unstructured ATL03 ICESat-2 photon retrievals. The GFT is applied to re-binned photon retrievals on 25 km segments for all six beams and outperforms a discrete Fourier transform (DFT) in accuracy while having fewer constraints on the data structure. The MH algorithm infers wave direction from beam pairs every 25 km using coherent crests of the most energetic waves. Assuming a dominant incident angle, both methods together allow a decomposition into 2D surface wave spectra with the advantage that the residual surface heights can potentially be attributed to other sea-ice properties. The combined GFT–MH method shows promise in routinely isolating waves propagating through sea ice in ICESat-2 data. We demonstrate its ability on a set of example ICESat-2 tracks, suggesting a detailed comparison against in situ data is necessary to understand the quality of retrieved spectra.

Coastal Data Information Program: advances in measuring and modeling wave activity, climate, and extremes

ABSTRACT The Coastal Data Information Program (CDIP) provides wave data to the public in near real-time, maintains an operational wave model for the California coast, and is engaged in ocean wave research on a global scale. CDIP’s array of moored wave buoy stations are instrumented with Datawell Waveriders. CDIP’s recent work to improve monitoring capabilities for directional surface wave spectra, surface current, and temperature is described. This includes data quality assurance and control, real-time alerts, telemetry and dissemination information technology infrastructure and methodology, data visualization tools, and mooring and instrumentation innovation. CDIP’s goal is to maximize data reliability, availability, accuracy, and precision. Validation of commonly used wave models – operational, hindcast, and forecast – with CDIP data is automated to provide assessments of relative skills at a variety of coastal locations and wave conditions. Wave heights measured by the buoys typically exceed modeled heights during the most energetic events, such as hurricanes, nor’easters, and bomb cyclones. In a practical validation example, the global wave model used to drive CDIP’s California coastal wave forecasts was recently changed, based on comparisons against buoy data. Forecast performance has improved for swell events, which are a challenge to model accurately in the Southern California Bight.

Source Parameters of Strong Turkish Earthquakes on February 6, 2023 (<i>M<sub>w</sub></i> = 7.8 and <i>M<sub>w</sub></i> = 7.7) from Surface Wave Data

Abstract—Based on the amplitude spectra of surface waves, the source parameters of the strong Turkish earthquakes of February 6, 2023 (Mw = 7.8 and Mw = 7.7) were calculated in two approximations: an instantaneous point source and an elliptical shear dislocation. As a result, rupture planes were identified, data were obtained on the scalar seismic moment, moment magnitude, focal mechanism, and source depth of the considered seismic events, and the integral parameters characterizing the rupture geometry and its development in time were estimated. It is shown that the sources of the earthquakes under study were formed under the influence of the regional stress field and their focal mechanisms were left lateral faults with a strike direction close to the strike of the East Anatolian fault zone for the first event and close to the strike of the Sürgü-Çardak fault system for the second. For the first earthquake, our estimates of the rupture duration and its length (t = 52.5 s, L = 180 km) probably refer not to the entire rupture, but only to its main phase, confined to the northeastern segments of the East Anatolian fault and characterized by maximum displacements and values of the released seismic moment. The values of t = 30 s and L = 180 km that we obtained for the second earthquake fully characterize the entire rupture.

Effect of Wave Directions on Orientation and Magnitude of Surface Wind Stress under Typhoon Megi (2010)

Abstract The relationship between the wind-wave spectrum and surface wind stress τ in tropical cyclones, especially for the misalignment |ϕ| between the wind and τ, was investigated using data from three Electromagnetic Autonomous Profiling Explorer (EM-APEX) floats deployed in Super Typhoon Megi (2010). The floats measured τ by integrating downward momentum flux in the ocean and, in a recent development, directional spectra of surface waves. The wind was captured by aircraft surveys. At wind speeds from 25 to 40 m s−1, the |ϕ| increased with the increasing angle between the wind and dominant waves. The |ϕ| was small near the eyewall, where wave energy concentrated in a narrow frequency band. At the location far away from the eyewall, where most spectra were bimodal in directions with similar frequencies, the stress direction might be similar to the high-frequency waves. The misalignment between the wind and propagating swell might affect the growth and directional spreading of wind waves under tropical cyclones. The resulting wave breaking might then release wave momentum into the ocean as most stress clockwise from the wind direction. C‖, the downwind drag coefficient, increased with increasing inverse wave age of dominant waves. |C⊥|, the magnitude of the crosswind drag coefficient, was significant when low-frequency waves deviated from the wind by more than 90°. The wave directions are used in the inverse wave age for scaling drag coefficients. The new parameterization based on wave dynamics can be useful for improving the prediction of wind stress curl under storms. Significance Statement Tropical cyclones can impact the maximum sea surface temperature cooling through the curl of surface wind stress τ, which causes divergence under the storm eye. To investigate the effect of surface waves on τ, measurements of downward momentum flux and surface waves from three EM-APEX floats deployed under Typhoon Megi in 2010 are used. The inverse wave age involving wind forcing on the wave directions of dominant waves and swells can significantly influence the momentum transfer efficiency in the downwind and crosswind directions, respectively. That is, the propagating swell under storms should play a crucial role in the downward momentum flux during its interaction with high-frequency waves and wind. Incorporating wave directions to parameterize the magnitude and orientation of τ will improve future models’ ability to predict wind stress curl and thereby the heat fluxes to storm intensification.

Surface wave height distributions and rogue wave probabilities on two-layer fluids

Rogue waves are individual ocean surface waves much larger than the prevailing wave field. In high sea states they can be a danger to marine operations. Rogue waves are well studied for unstratified water. However, on a two-layer fluid the surface wave spectra are modified due to triad interactions with interfacial waves. Such triad interactions are not possible in homogeneous water. We find the modified surface spectrum reduces rogue waves. These findings are relevant for the changing polar oceans where prolonged ice melt is expected to facilitate open water with higher sea states while also creating a surface layer of freshwater overlaying salt water, as in our idealized model calculations.

Analysis of Sound Fluctuations in Shallow Water in High Sea States

Sound intensity fluctuation plays a significant role in underwater acoustic studies. In this article, an experiment was conducted in the South China Sea using a buoy system that autonomously emitted and received sound signals to obtain data on sound fluctuations under different wind conditions (in windy weather) for about 179 h. Results showed that the fluctuation of the transmission loss in a fixed position reached up to 15–20 dB. Different potential reasons for this transmission loss fluctuation are analyzed. Using the wind speed data provided by the Earth system, the sea surface wave spectrum model, and the bubble layer model, the fluctuation of the transmission loss was simulated based on the modified Ramsurf sound propagation model. The simulation and experimental results were in good agreement with each other. Therefore, the fluctuation of the transmission loss due to wind-generated waves in high sea states should be considered while studying underwater communication, particularly in shallow water with a positive gradient sound velocity profile.

Direct Simulation of the Surface Manifestation of Internal Gravity Waves with a Wave–Current Interaction Model

Abstract Internal solitary waves in the ocean are characterized by the surface roughness signature of smooth and rough bands that are observable in synthetic aperture radar satellite imagery, which is caused by the interaction between surface gravity waves and internal wave–induced surface currents. In this work, we study the surface signature of an internal wave packet in deep water over a large range of spatial scales using an improved wave–current interaction model that supports a moving surface current corresponding to a propagating internal gravity wave. After validating the model by comparison to previously published numerical results by Hao and Shen, we investigate a realistic case based on a recent comprehensive field campaign conducted by Lenain and Pizzo. Distinct surface manifestation caused by internal waves can be directly observed from the surface waves and the associated surface wave steepness. Consistent with observations, the surface is relatively rough where the internal wave–induced surface current is convergent (∂U/∂x < 0), while it is relatively smooth where the surface current is divergent (∂U/∂x > 0). The spatial modulation of the surface wave spectrum is rapid as a function of along-propagation distance, showing a remarkable redistribution of energy under the influence of the propagating internal wave packet. The directional wavenumber spectra computed in the smooth and rough regions show that the directional properties of the surface wave spectra are also rapidly modulated through strong wave–current interactions. Good agreement is found between the model results and the field observations, demonstrating the robustness of the present model in studying the impact of internal waves on surface gravity waves. Significance Statement The purpose of this study is to better understand the physical processes leading to the bands of rough and smooth surface waves arising from internal gravity waves. The surface manifestation of internal gravity waves allows them to be measured remotely via surface imagery, which can provide insight into their nonlinear behavior and sources and fate and which can ultimately inform the local stratification for assimilation into larger-scale models. Our results highlight the application of wave–current interaction models to the study of the interaction of surface waves with internal gravity waves and indicate strong modulation of the surface wave spectra over relatively short time scales despite the long time scales associated with the internal wave propagation.

On the Use of Dual Co-Polarized Radar Data to Derive a Sea Surface Doppler Model—Part 1: Approach

This article proposes a Doppler velocity (DV) model based on dual co-polarized (co-pol) decomposition of a normalized radar cross section of an ocean surface on polarized Bragg scattering and nonpolarized (NP) radar returns from breaking wave components. The dual co-pol decomposition provides a quantitative description of resonant and NP scattering, as well as their dependence on the incident angle, azimuth, and wind speed. Subsequently, the contributions of the facet (resonant Bragg waves and breakers) velocities, tilt, and hydrodynamic modulations due to long waves to the resulting DV can be quantified. The tilt modulation contributions to DV are estimated using the measured/empirical tilt modulation transfer function (MTF). The hydrodynamic modulations are mostly dominated by wave breaking and are estimated using a semiempirical model based on in situ measurements. In addition to the VV and HH radar data, which are required for dual co-pol decomposition and tilt MTF estimates, the surface wave spectrum is required in the DV determination for a given radar observation geometry. In this article, qualitative and quantitative consistencies are presented between the model simulations and the empirical CDOP model. In a companion paper, a DV analysis is presented to analyze the Sentinel-1 synthetic aperture radar measurements and collocated in situ measurements of surface wind and wave spectra.

A niching particle swarm optimization strategy for the multimodal inversion of surface waves

SUMMARY In practice, near-surface structures with shear wave velocity inversions or strong shear wave velocity contrasts may cause the phase velocity spectra of surface waves to be complex. Hence, it is sometimes difficult to identify mode numbers in the phase velocity spectrum. To avoid numbering different modes, the determinant misfit function has been applied to invert multimodal dispersion curves with a very limited computational cost due to the absence of the root-seeking procedure. However, this function presents a complicated relation with modal parameters and thus has multiple minima, resulting in an increase in model ambiguity. Therefore, it is more appropriate to adopt a multimodal optimization algorithm to find multiple minima instead of obtaining one optimal solution. In this study, we use a niching particle swarm optimization to find multiple minima with an enhanced fine search ability. Subsequently, we performed cluster analysis to distinguish different clusters in the inverted solutions and find the best-fitting profiles from multiple minima based on the Euclidean distance between the measured and inverted dispersion curves. Moreover, a modified Thomson–Haskell transfer matrix method is used to calculate the determinant misfit function for a better constraint on inversion because it can only resolve the surface wave modes possessing energy at the free surface, where both the sources and geophones are commonly deployed for active and passive surface wave exploration. Tests of synthetic and field data demonstrate that our inversion method is both effective and robust and emphasize its great potential in urban subsurface exploration and geotechnical characterization applications.

Adapting ocean surface scattering models to accept in-situ environmental data

A renewed examination of the theoretical basis of rough sea surface scattering has unearthed uncertainty over what theoretical approach is best suited for realtime applications, as evaluated in terms of speed, accuracy, and ability to allow greater use of in situ environmental data. The investigation focused primarily on applied models, as related to signal scattering losses and to reverberation modeling. Modeling approaches compared include perturbation theory, the approach by Eckart, and the approaches examined at the University of Washington and the Naval Research Laboratory. Validation by comparisons to data will be cited as available. A design goal of many models is to require only a small number of easily observed environmental parameters, such as wind speed and significant wave height. This presentation explores the insertion of additional inputs that would support predictions more relevant to the specific time and place of the application. These inputs would include measured or simulated surface wave spectrum data and estimates of surface height coherence length.

Ocean Surface Wind Estimation From Waves Based on Small GPS Buoy Observations in a Bay and the Open Ocean

AbstractOcean surface wind and wave information is important in a wide variety of areas, such as coastal disaster reduction, offshore structure design, and atmosphere‐ocean flux estimation. This study proposed a new method for ocean surface wind estimation from surface wave spectrum information measured by small global positioning system buoys. The concept of this method relies on the assumption that the high‐frequency part of the ocean‐wave spectrum is proportional to where is the friction velocity and is the frequency. The determination algorithm for the coefficient of was optimized in this study. The wind direction was determined by the wave cross‐spectrum, assuming that the wind direction aligns the propagation direction of the high‐frequency part of the wave. The proposed wind estimation method was applied to bay and open ocean observations, and the performance of the proposed wind estimation method was similar between the bay and the open ocean. The proposed method improves the wind estimation especially in coastal areas and at high wind speeds in the open ocean compared with the previous method. The performance of the method of the previous study differs between the bay and open ocean due to their spectral shape differences. High‐quality wind and wave information can be obtained using the proposed method. If the mass deployment of small drifting buoys covered the global ocean, the information based on the proposed method could be considerably powerful, and could compensate for the weakness of satellite‐based wind and wave estimations.

Using Axial Base cabled array sensor data to study the prediction of second-order pressures from nonlinear surface wave interactions associated with microseisms

There are currently no published experimental measurements of second-order pressures in the water column from nonlinear surface wave interactions. Microseism researchers have focused on predicting and measuring microseisms directly without measuring second-order pressures in the water column. We considered several Ocean Observatory regional cabled arrays as sources for water column measurements to compare with analytical model second-order pressure predictions based on hindcast directional wave spectra. We selected the Axial Base cabled array for its location and suite of instruments including two hydrophones, 3D velocity sensor, and seismometer near the seafloor. Here we present results for predicted second-order pressures along with hydrophone measurements at the Axial Base site over different times of a year (2019–2020) to demonstrate a correlation. Validating a prediction model for second-order pressures based on directional surface wave spectra using the OOI cabled array sensor data could spur development of wave energy harvesting devices in the deep ocean and other applications.

Surface manifestation of stochastically excited internal gravity waves

ABSTRACT Recent photometric observations of massive stars show ubiquitous low-frequency ‘red noise’ variability, which has been interpreted as internal gravity waves (IGWs). Simulations of IGWs generated by convection show smooth surface wave spectra, qualitatively matching the observed red noise. Theoretical calculations using linear wave theory by Shiode et al. and Lecoanet et al. predict IGWs should manifest at the surface as regularly spaced peaks associated with standing g modes. In light of the apparent discrepancy between these theories and simulations/observations, we test the theories with simplified 2D numerical simulations of wave generation by convection. The simulations agree with the transfer function calculations presented in Lecoanet et al., demonstrating that the transfer function correctly models linear wave propagation. However, there are differences between our simulations and the g-mode amplitude predictions of Shiode et al. This is because that work did not take into account the finite width of the g-mode peaks; after correcting for this finite width, we again find good agreement between theory and simulations. This paper verifies the theoretical approach of Lecoanet et al. and strengthens their conclusion that IGWs generated by core convection do not have a surface manifestation consistent with observed low-frequency variability of massive stars.

KAGRA underground environment and lessons for the Einstein Telescope

The KAGRA gravitational-wave detector in Japan is the only operating detector hosted in an underground infrastructure. Underground sites promise a greatly reduced contribution of the environment to detector noise thereby opening the possibility to extend the observation band to frequencies well below 10 Hz. For this reason, the proposed next-generation infrastructure Einstein Telescope in Europe would be realized underground aiming for an observation band that extends from 3 Hz to several kHz. However, it is known that ambient noise in the low-frequency band 10 Hz - 20 Hz at current surface sites of the Virgo and LIGO detectors is predominantly produced by the detector infrastructure. It is of utmost importance to avoid spoiling the quality of an underground site with noisy infrastructure, at least at frequencies where this noise can turn into a detector-sensitivity limitation. In this paper, we characterize the KAGRA underground site to determine the impact of its infrastructure on environmental fields. We find that while excess seismic noise is observed, its contribution in the important band below 20 Hz is minor preserving the full potential of this site to realize a low-frequency gravitational-wave detector. Moreover, we estimate the Newtonian-noise spectra of surface and underground seismic waves and of the acoustic field inside the caverns. We find that these will likely remain a minor contribution to KAGRA's instrument noise in the foreseeable future.

Evanescent surface acoustic waves in 1D viscoelastic phononic crystals

In this paper, evanescent surface waves propagating in a one-dimensional surface phononic crystal are investigated. The phononic crystal consists of elastic pillars periodically arranged on a viscoelastic substrate. By using the finite element method, the complex band structures and transmission spectra of surface waves are calculated. It is found that the evanescent wave with π phase change of the real part lies inside the resonant bandgap, and no cusp is observed for the minimum imaginary part. With the increase of frequency, the surface waves can be gradually converted to bulk waves. When the pillar height is increased, the generation mechanism of the first bandgap gradually varies from Bragg scattering to local resonance, and the evanescent waves above the sound line can be reconstructed and shifted below the sound line. When the viscosity is introduced, the minimum imaginary part inside the bandgap decreases. However, the corresponding attenuation is strengthened because the contribution of the bulk wave to the transmission gets weak. The work in this paper is relevant to the practical application of surface waves.

Surface wave reflection from a metasurface termination

The reflection coefficient of a microwave surface wave incident at the termination of a metasurface is explored. Two different surface types are examined. One is a square array of square metallic patches on a dielectric-coated metallic ground plane, the other a Sievenpiper ‘mushroom’ array. In the latter the surface wave fields are more confined within the structure. Comparison of the measured surface-wave reflection spectra is made with that obtained from analytic theory and numerical modelling. The reflection coefficient is shown to be dependent on both the momentum mismatch between the surface wave and the freely propagating modes as well as the different field distributions of the two modes.

Nonlinear Wave Evolution in Interaction with Currents and Viscoleastic Muds

A numerical model is extended to investigate the nonlinear dynamics of surface wave propagation over mud in the presence of currents. A phase-resolving frequency-domain model for wave-current interaction is improved to account for wave modulations due to viscoelastic mud of arbitrary thickness. The model compares well with published laboratory data and performs slightly better than the model with viscous mud-induced wave damping mechanism. Monochromatic and random wave simulations are conducted to examine the combined effect of currents, mud-induced wave dissipation and modulation, and nonlinear wave-wave interactions on surface wave spectra. Results indicate that current effects on wave damping over viscoelastic mud is not as straightforward as that over viscous mud. For example, while opposing currents consistently increase damping of random waves over viscous mud, they can decrease damping over viscoelastic mud due to high variations in frequency-dependent damping stemming from mud’s elasticity. It is shown that a model that assumes the mud layer to be thin for simplification can overestimate wave damping over thick mud layers.