Wave Spectrum Research Articles

Site effects in seismic motion

We use the harmonic-oscillator model to analyze the motion of the sites (ground motion), seimograph recordings, and structures built on the Earth’s surface under the action of the seismic motion. The seismic motion consists of singular waves (spherical-shell P and S primary seismic waves) and discontinuous (step-wise) seismic main shocks. It is shown that these singularities and discontinuities are present in the ground motion, seismographs’ recordings and the motion of the built structures. In addition, the motion of the oscillator exhibits oscillations with its own eigenfrequency, which represent the response of the oscillator to external perturbations. We estimate the peak values of the displacement, the velocity and the acceleration of the ground motion, both for the seismic waves and the main shock, which may be used as input parameters for seismic hazard studies. We discuss the parameters entering these formulae, like the dimension of the earthquake focus, the width of the primary waves and the eigenfrequencies of the site. The width of the seismic waves on the Earth’s surface, which includes the energy loss, can be identified from the Fourier spectrum of the seismic waves. Similarly, the eigenfrequencies of the site can be identified from the spectrum of the site response. The paper provides a methodology for estimating the input parameters used in hazard studies.

Quantitative analysis of the gravitational wave spectrum sourced from a first-order chiral phase transition of QCD

We investigate the cosmological first-order chiral phase transition of quantum chromodynamics (QCD), and for the first time calculate its parameters which can determine the gravitational wave spectrum. With the state-of-the-art calculation from the functional QCD method, we found that the large chemical potential of QCD phase transition results in very weak and fast first-order phase transitions at the temperature lower than O(102) MeV. These results further suggest that the gravitational wave (GW) signals of NANOGrav are very unlikely sourced from the chiral phase transition of QCD. Published by the American Physical Society 2025

Gravitational waves induced by scalar perturbations with a broken power-law peak

We give an analytical approximation for the energy spectrum of the scalar-induced gravitational waves (SIGWs) generated by a broken power-law power spectrum, and find that both the asymptotic power-law tails and the intermediate peak contribute distinct features to the SIGW spectrum. Moreover, the broken power-law power spectrum has abundant near-peak features and our results can be used as a near-peak approximation that covers a wide range of models. Our analytical approximation is useful in the rapid generation of the SIGW energy spectrum, which is beneficial for gravitational wave data analysis.

A position and wave spectra dataset of Marginal Ice Zone dynamics collected around Svalbard in 2022 and 2023

Sea ice is a key element of the global Earth system, with a major impact on global climate and regional weather. Unfortunately, accurate sea ice modeling is challenging due to the diversity and complexity of underlying physics happening there, and a relative lack of ground truth observations. This is especially true for the Marginal Ice Zone (MIZ), which is the area where sea ice is affected by incoming ocean waves. Waves contribute to making the area dynamic, and due to the low survival time of the buoys deployed there, the MIZ is challenging to monitor. In 2022-2023, we released 79 OpenMetBuoys (OMBs) around Svalbard, both in the MIZ and the ocean immediately outside of it. OMBs are affordable enough to be deployed in large number, and gather information about drift (GNSS position) and waves (1-dimensional elevation spectrum). This provides data focusing on the area around Svalbard with unprecedented spatial and temporal resolution. We expect that this will allow to perform validation and calibration of ice models and remote sensing algorithms.

Wind-driven Sea Spectra Resilience as Statistical Attractor

We have observed numerically the resilience phenomenon for ocean wind-driven waves, where the wave spectra return to their original self-similar form after a strong perturbation. This self-similar behaviour is seen as the manifestation of a statistical attractor associated with generalized spectra of Kolmogorov–Zakharov. We have confirmed this interpretation through numerical simulations of random water wave field within the kinetic (Hasselmann) equation. This equation with specific source functions similar to those of conventional wave forecasting models exhibits families of exact self-similar solutions. These source functions minimize the “non-self-similar” background, allowing us to evaluate the “clean rates” of wave spectra resilience. We use the indices of the exact self-similar solutions as parameters for the attractors of numerical solutions in a two-dimensional phase space.

Seabed Liquefaction Risk Assessment Based on Wave Spectrum Characteristics: A Case Study of the Yellow River Subaqueous Delta, China

Seabed liquefaction induced by wave loading poses considerable risks to marine structures and requires careful consideration in marine engineering design and construction. Traditional methods relying on statistical wave parameters for analyzing random waves often underestimate the potential for seabed liquefaction. To address this underestimation, the present study employs field observations and numerical simulations to examine wave characteristics and liquefaction distribution across various wave return periods in the Chengdao Sea area of the Yellow River subaqueous delta. The research results indicated that the wave decay phase exhibited a higher liquefaction potential than the growth phase, primarily because of the prevalence of low-frequency swell waves. The China Hydrological Code Spectrum (CHC Spectrum) effectively captured the wave characteristics in the study area, with parameterization grounded in measured data. The poro-elastic wave–sediment interaction model further elucidated the liquefaction distribution under extreme wave conditions, revealing a maximum liquefaction depth exceeding 3 m and prominent liquefaction zones at water depths of 5–15 m. Notably, seabed properties emerged as a critical factor for liquefaction and overshadowed water depth, with non-liquefaction zones occurring at water depths of less than 15 m at high clay content, highlighting the general liquefaction risk of silty seabed. This study enhances understanding of the seabed liquefaction process and offers valuable insights into engineering safety.

Physics-guided deep learning for skillful wind-wave modeling.

Modeling sea surface wind-waves is crucial for both scientific research and engineering applications. Nowadays, the most accurate wave models are based on numerical methods, which primarily concern the wave spectrum evolution by solving wave action balance partial differential equations. These methods are computationally expensive and limited by incomplete physical representations of wave spectral evolution. Here, we present a deep learning-based wave model trained using observation-merged wave hindcasts. Guided by the physics knowledge that waves are either generated by local current winds or by remote historical winds, this method can directly model significant wave height, bypassing the need for wave spectral information. This feature engineering effectively reduces the complexity of model inputs and outputs. The resulting artificial intelligence method can model 1 year of global significant wave heights at a 0.5° × 0.5° × 1-hour resolution within half an hour on a personal computer, achieving higher accuracy than state-of-the-art numerical wave models.

Investigation of Acoustic Waves generated by the Detonation Gun of a Zenith-M modernized Powerful Antihail Station

In this paper, a detonation gun of an antihail station was used to study acoustic waves as they propagated upward. The station's power was enhanced by placing a Hartmann resonance tube into the conical nozzle of the gun. Propagation speed, pressure-time waveform, and acoustic spectrum of the acoustic waves were determined. The propagation speed was approximately 890 m/s (Mach number ~2.6), and the initial (near-ground) intensity was 130-160 dB in the low-frequency range up to 200 Hz, where the energy distribution is relatively uniform. The results show that the antihail station can effectively influence atmospheric processes, either promoting rain precipitation or preventing hail formation.

Exploring seismic warning thresholds for vehicle-track systems through combined shaking table tests and dynamic numerical simulations

This study conducted vehicle-track shaking table model tests at the Seismic Laboratory of the China Academy of Building Research, employing both unidirectional (horizontal) and bidirectional (horizontal and vertical) seismic waves. Discussions were made on the dynamic response of the vehicle-track system and the mechanism of derailment, providing data support for the research on seismic early warning thresholds for vehicles. Additionally, three-dimensional finite element numerical simulations were performed on the vehicle-track dynamic model, successfully incorporating track irregularities into the model. In this paper, the main conclusions are as follows: The limits of the wheel load reduction rate and that of the derailment coefficient specified in China’s national standard “Code for Dynamic Performance Evaluation and Test Identification of Railway Vehicles” are conservative. The primary cause of vehicle derailment was identified as horizontal vibration of the track structure induced by seismic activity. Different seismic waves have varying effects on the dynamic response of the vehicle-track model, necessitating further research on the impact of seismic wave spectrum characteristics on vehicle safety during operation. When horizontal and vertical seismic waves are simultaneously applied, horizontal seismic waves have a greater impact on dynamic response. The numerical simulation results align well with experimental results, confirming the accuracy of the vehicle-track dynamic numerical model. It is recommended to adopt a more conservative seismic early warning threshold of 0.04 g to ensure the safety of train operation.

Simulation study on supercontinuum broadening based on the BIC model.

Bound states in the continuum (BIC) refers to waves that are entirely confined within the continuous spectrum of radiation waves without interacting with them. In our study, we attempted to construct a waveguide satisfying BIC conditions by forming a polymer layer on a 4H-SiC substrate, positioned on an S i O 2 insulator. By fine-tuning the waveguide parameters, we minimized losses to the substrate continuum and determined that the lowest loss meeting BIC conditions occurs when the HSQ width is 1.82µm and the 4H-SiC thickness is 440nm. Subsequently, we investigated the supercontinuum generation (SCG) in this waveguide. First, we analyzed the primary linear and nonlinear effects in the SCG process, introducing well-established theoretical frameworks such as the generalized nonlinear Schrödinger equation (GNLSE) for pulse propagation in nonlinear media. We then studied the influence of waveguide parameters on SCG, observing the variations in SCG with different HSQ widths and 4H-SiC thicknesses. Our results indicate that optimal spectral broadening and conversion efficiency are achieved with an HSQ width of 1.82µm and a 4H-SiC thickness of 440nm. In our simulations, the waveguide length was set to 1cm, and the pump pulse was modeled as a Gaussian pulse with a width of 100fs and a peak power of 8W.

Dynamic Response and Fatigue Analysis of a New Marine Gravitational Energy Storage System Under Wave Loads

Given the unstable input of electricity generated by offshore renewable energy in connection to the power grid at present, one solution is energy storage technology. In recent years, the new marine gravitational energy storage technology has received wide attention in China and worldwide. To apply this new energy storage technology for use in the ocean, in view of the structural characteristics of the new offshore gravitational energy storage system, a support structure based on the foundation of a wind-powered pipe frame is proposed. In order to verify the feasibility of the support structure, a finite element model is established using SACS to analyze whether it meets the requirements. The construction of this structure in a specific sea is simulated through finite element simulation. Then, in accordance with the hydrogeological conditions of the sea area, the wind turbine data, and the dimensional parameters of the energy storage system’s structure, a finite element model is established with SACS for static analysis, modal analysis, random wave response analysis, and wave spectrum fatigue analysis, thereby determining whether the structure meets the requirements for strength, deformation, and fatigue. The research results show that the UC value of the static strength of the support structure of the new offshore gravitational energy storage system is less than 1. In the modal analysis, the natural frequencies of the first- and second-order modes are not within the danger range. In the corresponding random wave analysis, it is found that the natural frequencies of the first four orders are the greatest contributors to the dynamic response during the normal operation of the turbine. In fatigue analysis, it is concluded that the structure meets all the requirements of DNV specifications. The research results provide a reference for the engineering application of the support structure of the new gravitational energy storage system in the ocean.

Investigating nearshore spatial and temporal trends in nutrient concentrations along an urban northern shoreline, Lake Ontario

The nearshore zone of the Laurentian Great Lakes is of significant ecological importance, providing critical biogeochemical processes supporting spatially diverse habitats for a variety of species. Extreme plant and algal growth are common due to excessive anthropogenic eutrophication, with exacerbations from dreissenid establishment and lake mixing (e.g., coastal upwelling events and nearshore-offshore water exchanges), resulting in nuisance algal blooms across the nearshore area adjacent to Western Durham, Ontario, Canada. Thus, our main goal was to characterize the trends in essential nutrients (i.e., phosphorus and nitrogen) within the nearshore by applying general additive models on irregular time-series from 2011 to 2022 and to identify plausible contributing factors using exploratory principal component analysis. Increasing trends for total phosphorus were observed in surface (0.5 m below the surface) and benthic (0.5 m above the bottom) waters despite decreases in point source loading to the area. Most notably, the local water pollution control plant (WPCP) outfall did not seem to drive lake phosphorus concentrations across the study area, depicted by an orthogonal relationship within the principal component analysis. While the WPCP is a point source to the nearshore, it does not appear to be the primary driver of temporal lake phosphorus trends. Our results suggest that weather, inertial forcings and lake hydrodynamics in combination with traditional point-sources across Western Durham are contributing to the increasing total phosphorus trends observed as the peak period of wave spectra, wave height, alongshore wind speeds, watershed loadings, and total phosphorus concentrations within Lake Ontario were positively associated.

Structure formation with primordial black holes: collisional dynamics, binaries, and gravitational waves

Primordial black holes (PBHs) could compose the dark matter content of the Universe. We present the first simulations of cosmological structure formation with PBH dark matter that consistently include collisional few-body effects, post-Newtonian orbit corrections, orbital decay due to gravitational wave emission, and black-hole mergers. We carefully construct initial conditions by considering the evolution during radiation domination as well as early-forming binary systems. We identify numerous dynamical effects due to the collisional nature of PBH dark matter, including evolution of the internal structures of PBH halos and the formation of a hot component of PBHs. We also study the properties of the emergent population of PBH binary systems, distinguishing those that form at primordial times from those that form during the nonlinear structure formation process. These results will be crucial to sharpen constraints on the PBH scenario derived from observational constraints on the gravitational wave background. Even under conservative assumptions, the gravitational radiation emitted over the course of the simulation appears to exceed current limits from ground-based experiments, but this depends on the evolution of the gravitational wave spectrum and PBH merger rate toward lower redshifts.

A Study into the Effect of Hull Configuration on the Performance of Floating Solar PV Structure

At present, energy transition is a reality in the journey towards achieving net zero emission. Among others, the development of floating solar photovoltaic (FPV) power plants is one of many possible renewable energy technologies that received considerable attention. One of the reasons for that is attributed to land acquisition which can lead to conflicts, whilst the use of sea is more flexible. Therefore, the development of floating solar PV situated at the near shore (later can be moved offshore) is promising particularly in order to withstand the harsh environment. The study aims to demonstrate such an innovative design of a floating structure and two types of hulls (monohull and twin-hull) are considered and focused on the seakeeping performance of the two bodies. BEM approach with Green-Function based on the 3-D diffraction panel method together with the use of the Joint North Sea Wave Project (JONSWAP) wave spectrum is carried out to accomplish the seakeeping characteristic. The final computational simulation results show that the twin-hull model has more advantages than the monohull design. The trend of the RAO pattern, response spectra, and significant response for heave and pitch motion represent only slight differences between the two proposed designs. However, substantial disparity emerges in roll motion, with the difference in response values in prevailing 0o -roll heading standing at 53%, 39%, 27%, and 18% for sea states 1 through 4, respectively. Moreover, in 45o wave heading (quartering sea) it demonstrates a slightly lower disparity compared to the 0o wave heading (following sea) through sea-state 1-4 standing for 50%, 37%, 24% and 16% respectively.

Simulation of time-invariant three-dimensional Freak waves and their scattering identification based on the JONSWAP spectrum and Donelan direction function

Abstract Investigations into recent maritime accidents have revealed that a significant number are linked to the impact of freak waves, which possess the potential to capsize vessels rapidly due to their immense energy. In order to detect and predict these freak waves with precision, thereby mitigating the risks they pose to maritime infrastructure and human safety, we have delved deeper into the study of such waves. This paper introduces an effective and time-invariant three-dimensional (3D) computational model for freak waves. The model is designed to analyze the scattering properties of these waves and to provide a clearer understanding of the variations in their scattering behavior. First, this paper adopts linear superposition method to simulate a 3D random rough sea surface based on the JONSWAP wave spectrum and Donelan directional distribution function. Moreover, we analyze the effect of different angular frequencies on the simulated sea surface. At the same time, the Monte Carlo method is used to further simulate the capillary waves based on the random sea surface, and this method vastly improves the computational accuracy of the random sea surface. Then, based on the two-wave train superposition wave energy focusing mode, a numerical calculation method of time-invariant 3D freak waves is proposed, and the time-series evolution process of 3D freak waves is simulated. Finally, the backscattering coefficients of the 3D freak wave surface are calculated using the two-scale method, and the electromagnetic scattering characteristics of the freak wave surface under different evolution stages, wind speeds, and radar incidence angles are analyzed. By this method, we conclude that the recognition of freak waves is more accurate under medium-high wind speed and significant incidence angle conditions. Our experimental findings demonstrate that the methodologies presented in this study are capable of enhancing the identification and prediction of freak waves. This advancement is expected to bolster the precision of future freak wave forecasts and holds potential for practical application in the realm of freak wave risk alert systems.

Magnetospheric Control of Ionospheric TEC Perturbations via Whistler-Mode and ULF Waves.

The weakly ionized plasma in the Earth's ionosphere is controlled by a complex interplay between solar and magnetospheric inputs from above, atmospheric processes from below, and plasma electrodynamics from within. This interaction results in ionosphere structuring and variability that pose major challenges for accurate ionosphere prediction for global navigation satellite system (GNSS) related applications and space weather research. The ionospheric structuring and variability are often probed using the total electron content (TEC) and its relative perturbations (dTEC). Among dTEC variations observed at high latitudes, a unique modulation pattern has been linked to magnetospheric ultra-low-frequency (ULF) waves, yet its underlying mechanisms remain unclear. Here using magnetically conjugate observations from the THEMIS spacecraft and a ground-based GPS receiver at Fairbanks, Alaska, we provide direct evidence that these dTEC modulations are driven by magnetospheric electron precipitation induced by ULF-modulated whistler-mode waves. We observed peak-to-peak dTEC amplitudes reaching 0.5 TECU (1 TECU is equal to electrons/ ) with modulations spanning scales of 5-100km. The cross-correlation between our modeled and observed dTEC reached 0.8 during the conjugacy period but decreased outside of it. The spectra of whistler-mode waves and dTEC also matched closely at ULF frequencies during the conjugacy period but diverged outside of it. Our findings elucidate the high-latitude dTEC generation from magnetospheric wave-induced precipitation, addressing a significant gap in current physics-based dTEC modeling. Theses results thus improve ionospheric dTEC prediction and enhance our understanding of magnetosphere-ionosphere coupling via ULF waves.

Black Holes and Gravitational Waves from Slow First-Order Phase Transitions.

Slow first-order phase transitions generate large inhomogeneities that can lead to the formation of primordial black holes. We show that the gravitational wave spectrum then consists of a primary component sourced by bubble collisions and a secondary one induced by large perturbations. The latter gives the dominant peak if β/H_{0}<12, impacting, in particular, the interpretation of the recent pulsar timing array data. The gravitational wave signal associated with a particular primordial black hole population is stronger than in typical scenarios because of a negative non-Gaussianity of the perturbations, and it has a distinguishable shape with two peaks.

Array Optimization for a Wave Energy Converter with Adaptive Resonance Using Dual Bayesian Optimization

A novel Dual Bayesian optimization strategy is formed for an array of wave energy converters with adaptive resonance to maximize the annual performance through the energy conversion processes from irregular waves to electricity. A wave energy converter with adaptive resonance changes the natural frequency of power take-off dynamics for varying irregular waves, resulting in the maximum annual energy production. The first step of the two-step Dual Bayesian optimization determines the geometric layout of the array, which maximizes the first energy conversion to the total array excitation for irregular waves occurring annually. The second step optimizes the operational parameters of individual wave energy converters in the optimized array to maximize the power generation in varying sea states through simultaneous conversion to mechanical and electrical energy. The coupled hydrodynamics are solved in the frequency domain, and the power performance is evaluated by solving the Cummins’ equation in the time domain extended for multiple floating bodies, each strongly coupled with nonlinear power take-off dynamics. The proposed method is applied to a surface-riding wave energy converter, already optimized for single unit operation at individual sea states. Investigating two array layouts, linear and random, the optimized arrays after Step 1 increase the excitation spectral area by up to 40% relative to the single unit operation, indicating the synergy enhancing the first energy conversion. Subsequently, the dual-optimized linear layout attained a q-factor up to 1.13 in commonly occurring sea states, achieving improved average power generation in 60% of the evaluated sea states. The performance of the random layout exhibited the average power fluctuating along the wave spectra with a peak q-factor of 1.07. The individual adaptive resonance is confirmed in the optimized arrays, such that each surface-riding wave energy converter of both layouts adaptively resonates with the peak of the wave excitation spectra, maximizing the power generation for the different irregular waves.

Short-term wave forecasting for offshore wind energy in the Baltic Sea

The increasing interest in ocean-based renewable energy sources and the consequent need for advanced marine infrastructure have heightened the demand for accurate short-term forecasting of significant wave height (SWH). Given the impending investments in offshore infrastructure within the Baltic Sea, it becomes imperative to devise artificial intelligence strategies that can accurately predict wave parameters under the unique conditions of a shallow, tideless sea. This study presents an extensive evaluation of established machine learning techniques tailored to site specific wave spectra. We explore the effectiveness of artificial neural networks (ANNs) in the short-term prediction of SWH. Rigorous optimization of neural network hyperparameters is applied to improve forecast accuracy, with models validated on real-world datasets, proving their ability to predict SWH accurately across various forecast horizons. In addition, the performance of ANNs models is compared to optimized traditional forecasting methods, noting significant improvements in both accuracy and reliability. The results underscore the critical role of careful optimization in achieving precise short-term forecasts at targeted locations. They also suggest that even relatively simple models, when fine-tuned, can surpass the performance of more complex approaches commonly found in the literature. Building upon the foundational advancements in ANNs from the early 2000s, this research adopts a direct forecasting methodology utilizing data from marine observational platforms. Significantly, the networks are trained and validated with data directly obtained from a measurement buoy positioned in a deep water zone, devoid of seabed wave interactions. This aspect is particularly crucial for the strategic placement of future floating offshore farms, where these algorithms will be directly applied for short-term SWH predictions. Our findings underscore the importance of selecting optimal methods to ensure the utmost accuracy of short-term forecasts at targeted locations.

Fingerprinting Magnetic States in Interconnected Nanoring Arrays via Spin Wave Spectra

Arrays of interconnected magnetic nanorings show emergent dynamics arising from stochastic interactions at junctions between rings. These global emergent properties have already shown potential as a platform for reservoir computing. However, their experimental computational performance has been limited by the use of a single-dimensional global measurement, their magnetoresistance, as an output, masking much of the underlying state information. Here, we show in both simulation and experiment the potential of using the spin wave spectra of such arrays of nanorings to produce a fingerprint of the number and orientation of the internal magnetic states, providing a route towards a multi-dimensional output with which to perform computation. We show that the spectra fulfill the two criteria for reservoir computing: a nonlinear response to an input stimulus, and a fading memory.