Wave Model Research Articles

Superposition and Interaction Dynamics of Complexitons, Breathers, and Rogue Waves in a Landau–Ginzburg–Higgs Model for Drift Cyclotron Waves in Superconductors

This article implements the Hirota bilinear (HB) transformation technique to the Landau–Ginzburg–Higgs (LGH) model to explore the nonlinear evolution behavior of the equation, which describes drift cyclotron waves in superconductivity. Utilizing the Cole–Hopf transform, the HB equation is derived, and symbolic manipulation combined with various auxiliary functions (AFs) are employed to uncover a diverse set of analytical solutions. The study reveals novel results, including multi-wave complexitons, breather waves, rogue waves, periodic lump solutions, and their interaction phenomena. Additionally, a range of traveling wave solutions, such as dark, bright, periodic waves, and kink soliton solutions, are developed using an efficient expansion technique. The nonlinear dynamics of these solutions are illustrated through 3D and contour maps, accompanied by detailed explanations of their physical characteristics.

Exact Model of Gravitational Waves and Pure Radiation

An exact non-perturbative model of a gravitational wave with pure radiation is constructed. It is shown that the presence of dust matter in this model contradicts Einstein’s field equations. The exact solution to Einstein’s equations for gravitational wave and pure radiation is obtained. The trajectories of propagation and the characteristics of radiation are found. For the considered exact model of a gravitational wave, a retarded time equation for radiation is obtained. The obtained results are used to construct an exact model of gravitational wave and pure radiation for the Bianchi type IV universe.

Wind stress modification by offshore wind turbines: A numerical study of wave blocking impacts

Offshore wind energy, as a clean and renewable resource, offers numerous advantages over onshore wind energy due to higher wind speeds and greater turbine capacity. However, the inadequate representation of wave-atmosphere interaction within the marine-atmospheric boundary layer may constrain wind resource assessments and, consequently, the design and layout of offshore wind turbines. By using the third-generation spectral wave model WAVEWATCH III, high-resolution numerical experiments which are capable of resolving the wind turbine foundation have been conducted to explore the blocking impact of wind turbine foundation on downstream wind stress. The findings provided significant insights into the factors influencing this effect, including foundation diameter, sea state, water depth, and wave directional spreading. Specifically, higher model resolution enables a more detailed characterization of wind stress distribution behind wind turbines. Increasing the foundation diameter resulted in a reduction of downstream wind stress. Notably, changes in wind stress exhibit a strong dependence on the sea state. The use of double periodic boundary conditions for the simulation domain enables an approximate representation of the entire wind farm by using a single turbine. Model results indicate that after waves pass through 20 turbines, domain-averaged wind stress decreases by approximately 3%, a figure that increases to 6% after passing through 50 turbines. The findings suggest the need to explore to what extent the changes in wind stress can alter wind profiles and how to parameterize the blocking impact of turbine foundations in wave models. This could have significant implications for wind farm site selection and layout design.

Regionalized ensemble estimation of wave periods for assessing wave energy resources across Canada. Part I: Improved wave-period modelling methodology

Large-scale estimations of wave periods are desired for wave energy assessment, ocean engineering, and wave climate research. Long-term global wave data from satellite altimeters are routinely applied to the estimations. However, this is challenged by uncertainties in wave-period models (WPMs), inaccuracies in data, and simplifications in modeling. Additionally, there exists a gap in the comprehensive examination of the variational mechanisms governing wave periods or model performances. As an effort to address them, we innovate a macroscale regionalized ensemble wave-period modeling (MREWPM) method by optimizing four wave-period models, driven by enhanced altimeter-based REWS (regionalized ensemble wave simulation) estimates of wave heights and wind speeds, within a regionalization framework in macroscale water environments. Results show that MREWPM driven by REWS dataset outperforms existing methods and performs better at larger scales (e.g., in eliminating local-scale overestimation). WPMs are more accurate over remote, deep, and windy regions in cool seasons under metrics-, scale- and data-dependent variations of performances with driving factors (mainly geographical features). This study serves as a foundational contribution towards the enhancement of wave-period simulations, the advancement of understanding wave-period dynamics, and the scientific evaluation of wave energy at macroscales.

Numerical investigation of the refractive properties of near-horizontal shore platforms and their effects on harmonic and stationary wave patterns

Near-horizontal shore platforms display highly irregular plan shapes, but little is known about the way in which these irregularities influence the significant wave height (Hŝ) on the platforms and the frequency components of the nearshore wavefield. As ocean waves share akin refractive properties to light rays, it can be assumed that, similarly to optical lenses, shore platforms can separate waves according to their frequency depending on their geometry. Thus, we use a non-linear Boussinesq wave model to conduct harmonic and bispectral mode decomposition analyses to study the control of concave and convex platform edges over wind waves (WW: 0.125–0.33 Hz), swell waves (SW: 0.05–0.125 Hz) and infragravity (IG: 0.008–0.05 Hz) waves frequencies. For breaking and non-breaking waves, increasing the platform edge concavity intensified wave divergence and subsequent attenuation of SW and IG across the outer platforms, reducing Hŝ by up to 25 %. Increasing the platform edge convexity intensified focusing and amplification of SW and WW over the outer platforms, increasing Hŝ by up to 18 % and 55 % for breaking and non-breaking waves. In the presence of breaking, IG amplification was affected by wave divergence across the inner platform, a condition determined by a critical convex curvature threshold (K=1.8) balancing wave focusing from refraction and defocusing from breaking. We find that convex curvature can determine the relative dominance of WW, SW and IG across platforms. Alongshore, coherent wave interactions governed IG stationary patterns defined by a node near the platform centreline and two antinodes on either side of concave edges. A node was generated at the platform centreline, and two antinodes were observed on either side of the convex edges for K>1.8, with the opposite pattern observed for K<1.8. Such patterns likely result in alongshore variations in wave-generated currents and erosion shaping rock coasts.

Improvements in Wave Age-Based Sea and Swell Separation for Offshore Industry Applications

Abstract For offshore wind turbines, an accurate description of the wave conditions is crucial for their design, construction, installation, maintenance, and operation. Typical sea states in the open ocean are often a combination of wind-sea and swell systems which cannot be fully described by a single set of parameters. In such cases the wave conditions are better defined by separating and quantifying the individual wave systems. In this paper, the wave age method has been revisited, and a modification has been proposed to add more functionality to better describe the wind/wave alignment of the wind-sea. A qualitative analysis was performed using offshore spectral energy data from a global wave model. The analysis was carried out for four different geographical locations: the Philippine Sea, the North Sea, the Atlantic Ocean, and the Pacific Ocean. The analysis compares the wind-sea and swell partitions separated by the standard and modified wave age methods. It shows an improved description of the wind-sea compared to the standard equation, especially in the case of high wind speed events and where the wind-sea partition is expected to dominate most of the spectral energy.

Thermal Wave and Pennes’ Models of Bioheat Transfer in Human Skin: A Transient Comparative Analysis

The primary focus of this study is to analyze comparative heat transfer in a two-dimensional (2D) multilayered human skin using thermal waves and Pennes' bioheat transfer models. The model comprises the epidermis, dermis, hypodermis tissue, and inner cells, and aims to understand their response to microwave (MW) power and electromagnetic (EM) frequency. The system of equations involves EM wave frequency and bioheat equations and uses the finite element method (FEM) for solving. It encompasses a range of microwave power levels (4-16 W), frequencies (0.9-4 GHz), and exposure durations (0-180 s). It examines how MW power and frequency affect temperature predictions due to different relaxation times. The results are visually represented, illustrating microwave power dissipation, isothermal profiles within the skin tissue, temperature trends at several locations, relaxation times, specific absorption rate (SAR), and the mean surface temperature of the multilayered dermal cell. Thermal analysis shows that Pennes' equation predicts higher temperatures than the thermal wave model of bioheat transfer (TWMBT). A notable disparity in temperature evolution is observed between the two models, especially in high-frequency transient heating scenarios. The TWMBT forecasts a delay in heat transfer, offering valuable insights into the more realistic short-term thermal behavior that the classical Pennes' model fails to capture. This comparative study underscores the significance of selecting an appropriate bioheat transfer model for precise thermal analysis in biomedical applications, such as hyperthermia treatment and thermal diagnostics. The findings emphasize the potential of the TWMBT to enhance the accuracy of thermal treatments in clinical settings.

Traveling wave mode analysis of a coherence collapse regime semiconductor laser with optical feedback

A highly developed traveling wave model for a semiconductor laser system supports sophisticated mode analysis of the coherence collapse regime in semiconductor lasers with delayed optical feedback. The concept of instantaneous optical modes is used. Time-frequency representations of chaotic trajectories are constructed and interpreted. This involves synthesizing the calculated optical modes with their corresponding steady states, analysis of the mode driving and coupling sources, and field expansion into modal components. The results support detailed physical interpretation of the optical and radiofrequency spectra throughout the coherence collapse regime. This includes simulation results for the transition out of coherence collapse at high optical feedback. Also key frequencies observed in the radiofrequency spectrum of the chaotic output are linked to the modes that mix to generate them.

The Dynamics of the Smart City Development: From the First Wave Model to the Third Wave Model

The Dynamics of the Smart City Development: From the First Wave Model to the Third Wave Model

Impacts of Langmuir turbulence derived from a statistical wave model on the oceanic mean state in the North Atlantic

Impacts of Langmuir turbulence derived from a statistical wave model on the oceanic mean state in the North Atlantic

Nonlinear dispersion analysis using dynamic traveling wave model in chemical kinetics

Nonlinear dispersion analysis using dynamic traveling wave model in chemical kinetics

Ocean Wave Energy Conversion: A Review

The globally increasing demand for energy has encouraged many countries to search for alternative renewable sources of energy. To this end, the use of energy from ocean waves is of great interest to coastal countries. Hence, an assessment of the available resources is required to determine the appropriate locations where the higher amount of wave energy can be generated. The current paper presents a review of the resource characterizations for wave energy deployment. The paper gives, at first, a brief introduction and background to wave energy. Afterward, a detailed description of formulations and metrics used for resource characterization is introduced. Then, a classification of WECs (wave energy converters) according to their working principle, as well as PTO (power take off) mechanisms used for these WECs are introduced. Moreover, different sources for the long-term characterization of wave climate conditions are reviewed, including in situ measurements, satellite altimeters, and data reanalysis on one hand, and numerical simulations based on spectral wave models on the other hand. Finally, the review concludes by illustrating the economic feasibility of wave farms based on the use of the levelized cost of the energy index.

Modelling the Sea Surface of Cardigan Bay

The aim of this project was to model the sea surface of Cardigan Bay, to be able to expand upon QinetiQ’s current wave models, used within their radar assurance activities. The sea surface can cause unwanted detections, which is referred to as clutter. The sea is not the only source of clutter such as litter and birds, have an impact on the returns detected by the radar. This project explored two different approaches, modelling the propagation of waves and modelling the distribution of energy across the sea surface. The first approach explored two open source models, WAVEWATCH III and SWAN, and after having technical errors, two real world, existing examples of where these models were implemented were researched. This research showed a lot of promise, and would be worth expanding upon. The second approach looked into two recognised equations for calculating the energy density of the waves, and then calculating the significant wave height. Overall, modelling the propagation of waves would produce more representative results, particularly SWAN which was a model designed for coastal waters, however to set up the wave models fell outside of the scope of this project.

Exploring nuclear matter phase transition through $$p_T$$ spectra analysis using blast wave model with Tsallis statistics in proton–proton collisions

Exploring nuclear matter phase transition through $$p_T$$ spectra analysis using blast wave model with Tsallis statistics in proton–proton collisions

Marsh restoration in front of seawalls is an economically justified nature-based solution for coastal protection

A marsh-fronted seawall is a hybrid nature-based coastal protection solution because it attenuates wave energy, reduces erosion, and provides ecosystem services. However, we still have a limited understanding of how to quantify the marsh wave attenuation benefits for economic analysis. Here, we incorporate a prediction of wave attenuation that accounts for species-specific morphology and structural stiffness into a 1-D wave model and validate it with field measurements. Our results show that the wave attenuation varies by a factor of two across different vegetation species. Further, we performed a benefit-cost analysis, in which the economic benefits represent the environmental services value and avoided seawall heightening cost that would otherwise be required to deliver the same overtopping rate without vegetation. We applied the model to a real-world, marsh-fronted seawall design at Juniper Cove, Massachusetts. Although the benefit of marsh-fronted seawalls is sensitive to discount rate, they have benefit-cost ratios greater than one, indicating that it is an economically justified nature-based solution. Further, we found that wave attenuation and benefit-cost ratio are more sensitive to water depth than wave height. Our study demonstrates the importance of considering the coastal protection of marshes and economic benefits in one framework.

Higher‐order integrable models for oceanic internal wave–current interactions

AbstractIn this paper, we derive a higher‐order Korteweg–de Vries (HKdV) equation as a model to describe the unidirectional propagation of waves on an internal interface separating two fluid layers of varying densities. Our model incorporates underlying currents by permitting a sheared current in both fluid layers, and also accommodates the effect of the Earth's rotation by including Coriolis forces (restricted to the Equatorial region). The resulting governing equations describing the water wave problem in two fluid layers under a “flat‐surface” assumption are expressed in a general form as a system of two coupled equations through Dirichlet–Neumann (DN) operators. The DN operators also facilitate a convenient Hamiltonian formulation of the problem. We then derive the HKdV equation from this Hamiltonian formulation, in the long‐wave, and small‐amplitude, asymptotic regimes. Finally, it is demonstrated that there is an explicit transformation connecting the HKdV we derive with the following integrable equations of a similar type: KdV5, Kaup–Kuperschmidt equation, Sawada–Kotera equation, and Camassa–Holm and Degasperis–Procesi equations.

Non-Classical Heat Transfer and Recent Progress

Abstract Heat transfer in solids has traditionally been described by Fourier's law, which assumes local equilibrium and a diffusive transport regime. However, advancements in nanotechnology and the development of novel materials have revealed non-classical heat transfer phenomena that extend beyond this traditional framework. These phenomena, which can be broadly categorized into those governed by kinetic theory and those extending beyond it, include ballistic transport, phonon hydrodynamics, coherent phonon transport, Anderson localization, and glass-like heat transfer, among others. Recent theoretical and experimental studies have focused on characterizing these non-classical behaviors using methods such as the Boltzmann transport equation, molecular dynamics, and advanced spectroscopy techniques. In particular, the dual nature of phonons, exhibiting both particle-like and wave-like characteristics, is fundamental to understanding these phenomena. This review summarizes state-of-the-art findings in the field, highlighting the importance of integrating both particle and wave models to fully capture the complexities of heat transfer in modern materials. The emergence of new research areas, such as chiral and topological phonons, further underscores the potential for advancing phonon engineering. These developments open up exciting opportunities for designing materials with tailored thermal properties and new device mechanisms, potentially leading to applications in thermal management, energy technologies, and quantum science.

Efficient Bayesian inference and model selection for continuous gravitational waves in pulsar timing array data

Abstract Finding and characterizing gravitational waves from individual supermassive black hole binaries is a central goal of pulsar timing array experiments, which will require analysis methods that can be efficient on our rapidly growing datasets. Here we present a novel approach built on three key elements: (i) precalculating and interpolating expensive matrix operations; (ii) semi-analytically marginalizing over the gravitational-wave phase at the pulsars; (iii) numerically marginalizing over the pulsar distance uncertainties. With these improvements the recent NANOGrav 15 yr dataset can be analyzed in minutes after an O ( 1 h ) setup phase, instead of an analysis taking days–weeks with previous methods. The same setup can be used to efficiently analyze the dataset under any sinusoidal deterministic model. In particular, this will aid testing the binary hypothesis by allowing for efficient analysis of competing models (e.g. incoherent, monopolar, or dipolar sine wave model) and scrambled datasets for false alarm studies. The same setup can be updated in minutes for new realizations of the data, which enables large simulation studies.

A 45-year updating wind and wave hindcast over the Oman Sea and the Arabian Sea

This study focuses on developing a comprehensive and reliable wind and wave hindcast for the Oman Sea and Arabian Sea, spanning a significant 45-year period (1979–2024). The objective is to capture the intricate wind and wave climate of the region, characterized by distinct monsoon cycles and occasional tropical cyclones. The availability of extensive wave data over four decades would be an irreplaceable tool for researchers and engineers, enabling improved accuracy in extreme value analysis, sediment transport studies, and wave-induced current simulations. Despite limited field observations, all available measured data within the region were collected, analyzed for configuration of the models and utilized for model calibration and validation. The hindcast data was generated using the Weather Research and Forecasting (WRF) model for winds and WAVEWATCH III (WW3) model for waves, and evaluated against observational and measured wind and wave parameters. A comprehensive statistical analysis of the hindcast model's performance reveals adequate agreement with measured data, as evidenced by root mean square errors (RMSEs) of 1.23 m/s for wind speeds and 0.37 m for significant wave heights in average. These results underscore the model's reliability for research and engineering applications, particularly in the Arabian Sea, with a focus on the northern coastlines of the Oman Sea. The specific model configuration employed in this study holds significant potential for future investigations in the northern Indian Ocean, offering a valuable tool for understanding and predicting climatical conditions in this region.

Model-based estimation of heart movements using microwave Doppler radar sensor.

Heart rate is one of the most crucial vital signs and can be measured remotely using microwave Doppler radar. As the distance between the body and the Doppler radar sensor increases, the output signal weakens, making it difficult to extract heartbeat waveforms. In this study, we propose a new template-matching method that addresses this issue by simulating Doppler radar signals. This method extracts the heartbeat waveform with higher accuracy while the participant is naturally sitting in a chair. An extended triangular wave model was created as a mathematical representation of cardiac physiology, taking into account heart movements. The Doppler radar output signal was then simulated based on this model to automatically obtain a template for one cycle. The validity of the proposed method was confirmed by calculating the PPIs using the template and comparing their accuracy to the R-R intervals (RRIs) of the electrocardiogram for five participants and by analyzing the signals of eight participants in their natural state using the mathematical model of heart movements. All measurements were conducted from a distance of 500 mm. The correlation coefficients between the RRIs of the electrocardiogram and the PPIs using the proposed method were examined for five participants. The correlation coefficients were 0.93 without breathing and 0.70 with breathing. This demonstrates a higher correlation considering the long distance of 500 mm, and the fact that body movements were not specifically restricted, suggesting that the proposed method can successfully estimate RRI. The average correlation coefficients, calculated between the Doppler output signals and the templates for each of the eight participants, exceeded 0.95. Overall, the proposed method showed higher correlation coefficients than those reported in previous studies, indicating that our method performed well in extracting heartbeat waveforms. Our results indicate that the proposed method of remote heart monitoring using microwave Doppler radar demonstrates higher accuracy in estimating the RRI of the electrocardiogram while at rest sitting in a chair, and the ability to extract the heartbeat waveforms from the measured Doppler output signal, eliminating the need to create templates in advance as required by conventional template matching methods. This approach offers more flexibility in the measurement environment than conventional methods.