Wave Model Research Articles

On smooth and peaked travelling waves in a local model for shallow water waves

We introduce a new model equation for Stokes gravity waves based on conformal transformations of Euler's equations. The local version of the model equation is relevant for the dynamics of shallow water waves. It allows us to characterize the travelling periodic waves both in the case of smooth and peaked waves and to solve the existence problem exactly, albeit not in elementary functions. Spectral stability of smooth waves with respect to co-periodic perturbations is proven analytically based on the exact count of eigenvalues in a constrained spectral problem.

Analysis of Spatial Dependence Using the Wave Covariance Structure in Soybean Productivity Associated With Soil Attributes

Objective: The aim of this study is to investigate the interaction between soybean yield and the physical and chemical attributes of the soil, with the goal of developing techniques used in precision agriculture to increase productivity, reduce costs, and minimize environmental impacts. Theoretical Framework: This work is based on the principles of geostatistics, particularly the Wave spatial dependence structure, which is used to model the semivariance function when it exhibits the "hole effect." Method: The research involves a study of soybean yield conducted in a commercial area of 172.04 hectares during the 2022/2023 growing season. Calcium (Ca), copper (Cu), acidity (pH), potassium (K), phosphorus (P), and soil penetration resistance (SPR) levels were used as covariates to explain soybean yield (Prod) through a Gaussian linear spatial model (GLSM). The Thin Plate Spline (TPS) interpolation method was applied to interpolate the physical and chemical soil attributes, considered as fixed covariates, while soybean yield was interpolated using External Drift Kriging (EDK) based on the GLSM. Additionally, techniques for local influence diagnostics were developed and applied to identify observations impacting the results, utilizing the Wave geostatistical model. Results and Discussion: The results revealed that the generated soybean yield map provides important information for defining management zones, optimizing input use, and promoting greater profitability. Furthermore, the removal of locally influential observations alters parameter estimation, the significance of parameters associated with the covariates in the GLSM, and the construction of the interpolated soybean yield map. In the discussion, the results were contextualized in light of the theoretical framework, emphasizing the relevance of the Wave structure and the integration of interpolation techniques in the study of spatial variability. Research Implications: The practical and theoretical implications of this research include improvements in agricultural management by providing support for the delineation of management zones that balance productivity and sustainability. Theoretically, the study contributes to advancing the use of geostatistical models, such as the Wave model, in the analysis of spatial data in precision agriculture. Originality/Value: This study contributes to the literature by exploring the application of the Wave model in an agricultural context, combined with the use of interpolation techniques and local influence diagnostics. Its originality lies in the methodological combination of spatial interpolators and the development of local influence techniques.

A wave-resolving two-dimensional vertical Lagrangian approach to model microplastic transport in nearshore waters based on TrackMPD 3.0

Abstract. Potentially acting as a source or a sink for plastic pollution to the open ocean, nearshore waters remain a challenging context for predicting the transport and deposition of plastic debris. In this study, we present an advanced modeling approach based on the SWASH wave model and the TrackMPD (v3.0) particle transport model to investigate the transport dynamics of floating and sinking microplastics in wave-dominated environments. This approach introduces novel features such as coupling with advanced turbulence models, simulating resuspension and bedload processes, implementing advanced settling and rising velocity formulations, and enabling parallel computation. The wave laboratory experiments conducted by Forsberg et al. (2020) were simulated to validate the model's ability to reproduce the transport of diverse microplastics (varying in density, shape, and size) along a comprehensive beach profile, capturing the whole water column. Our results underscore the robustness of the proposed model, showing good agreement with experimental data. High-density microplastics moved onshore near the bed, accumulating in proximity to the wave-breaking zone, while the distribution of low-density particles varied along the coastal profile depending on the particle properties. The study also sheds light on the primary mechanisms driving microplastic transport, such as Stokes drift, wave asymmetry, and settling/rising velocities. Sensitivity analyses on calibration parameters further confirm the robustness of the model results and the influence of these factors on transport patterns. This research establishes the SWASH–TrackMPD approach as a valuable tool, opening avenues for future studies to contextualize laboratory findings within the complexities of real-world nearshore environments and further refine our comprehension of microplastic dynamics across different beaches and wave-climate conditions.

Rutting Caused by Grouser Wheel of Planetary Rover in Single-Wheel Testbed: LiDAR Topographic Scanning and Analysis

This paper presents datasets and analyses of 3D LiDAR scans capturing the rutting behavior of a rover wheel in a single-wheel terramechanics testbed. The data were acquired using a LiDAR sensor to record the terrain deformation caused by the wheel’s passage through a Toyoura sandbed, which mimics lunar regolith. Vertical loads of 25 N, 40 N, and 65 N were applied to study how rutting patterns change, focusing on rut amplitude, height, and inclination. This study emphasizes the extraction and processing of terrain profiles from noisy point cloud data, using methods like curve fitting and moving averages to capture the ruts’ geometric characteristics. A sine wave model, adjusted for translation, scaling, and inclination, was fitted to describe the wheel-induced wave-like patterns. It was found that the mean height of the terrain increases after the grouser wheel passes over it, forming ruts that slope downward, likely due to the transition from static to dynamic sinkage. Both the rut depth at the end of the wheel’s path and the incline increased with larger loads. These findings contribute to understanding wheel–terrain interactions and provide a reference for validating and calibrating models and simulations. The dataset from this study is made available to the scientific community.

SFY — A lightweight, high-frequency and phase-resolving wave-buoy for coastal waters

Abstract Small lightweight wave buoys, SFYs, designed to operate near the coast, have been developed. The buoys are designed to record and transmit the full time series of surface acceleration at 52 Hz. The buoy uses the cellular network to transfer data and position (up to 80 km from the base station). This reduces costs and increases band-width. The low cost and low weight permits the buoys to be deployed easily, and in arrays in areas where satellite and wave models struggle to resolve wave and current interaction. The buoys are tested in a wave-flume, the open water and in the breaking waves of the surf. The conditions range from calm to significant wave heights exceeding 7 m and crashing breakers with accelerations exceeding 10g. The high sample rate captures the impulse of breaking waves, and allows them to be studied in detail. Breaking waves are measured and quantified in the open water. We measure breaking waves in the surf and recover the trajectory of waves breaking in the field to a higher degree than previously done. The time series of surface elevation, and accurate positioning, permits the signal of adjacent buoys to be correlated in a coherent phase-resolved way. Finally, we offer an explanation and solution for the ubiquitous low-frequency noise in IMU-based buoys and discuss necessary sampling and design to measure in areas of breaking waves.

Trajectory equations of interaction and evolution behaviors of a novel multi-soliton to a (2+1)-dimensional shallow water wave model

Trajectory equations of interaction and evolution behaviors of a novel multi-soliton to a (2+1)-dimensional shallow water wave model

Wind‐Wave Momentum Flux in Steep, Strongly Forced, Surface Gravity Wave Conditions

AbstractThe airflow separation from the water surface strongly impacts the coupling between wind and waves. To visualize the airflow and quantify the potential airflow separation's effect on the momentum transfer from wind to the wave, we conducted colocated sampling of air pressure, airflow, and water elevation under a range of wind and wave conditions in the laboratory. The experiments were conducted in the SUrge‐STructure‐Atmosphere INteraction (SUSTAIN) facility at the University of Miami. Three background wave conditions were subjected to wind forcing ( 5–16 m ) to investigate the effects of wave amplitude, frequency, and wind forcing on the airflow regime and momentum transfer. We found the wind forcing shifts the phase of the wave‐induced pressure fluctuations, enhancing the momentum transfer. An increase in wave amplitude or frequency also enhances the aerodynamic sheltering and the momentum transfer. The airflow‐derived pressure based on the nonseparated sheltering (NSS) hypothesis accounts for more than 90% of the momentum transfer until potential airflow separation. We found that the potential airflow separation over the waves' leeward face, which is not accounted for by the NSS hypothesis, leads to an underestimate in momentum transport of more than 30% than the actual value of momentum transport obtained from pressure measurements. Our wave growth rate is consistent with the revisited Miles theory that incorporates the wave‐induced Reynolds stress. The results of this work help explain the wave growth mechanism and inform the development of wind input functions for numerical wave models that account for airflow separation.

Optimized Wave Model Describing Infected Cases and Deaths of COVID-19 and Its Variants in Egypt

Optimized Wave Model Describing Infected Cases and Deaths of COVID-19 and Its Variants in Egypt

The 20‐Year Highest Tropical Cyclone‐Generated Waves Associated With the Maximum Energy of Seismic Noises

AbstractThe extreme winds of tropical cyclones generate high waves over the ocean, causing severe damage to offshore facilities and coastal communities. Disaster mitigation requires accurate prediction and forecasting of the highest potential waves. However, the physics of wave development is not fully understood, and the number of mid‐ocean observations during extreme tropical cyclones is extremely insufficient. Therefore, physically and statistically evaluating the highest potential waves is difficult. However, ocean waves excite seismic noise (microseisms). Although source sites of microseisms under specific tropical cyclones have been identified by case studies, the extreme ocean wave magnitude under tropical cyclones have not been systematically analyzed using long‐term historical records. Here, we, for the first time, utilize long‐term microseisms observed by seismic observation networks to associate the historical maximum microseisms events with the highest tropical cyclone‐generated wave events around Japan. We show that Typhoon Wipha in 2013, Typhoon Lan in 2017, and Typhoon Hagibis in 2019 were the maximum microseisms events in the past 20 years based on microseism energy within an 8–10 s period. We associate the events with the highest wave heights and the largest wave‐induced sea surface pressures generated by tropical cyclones. Although ocean wave models have a large uncertainty of tropical cyclone‐generated extreme waves, microseisms observations can endorse the results of an ocean wave model even if lack of direct ocean wave observation under tropical cyclones. Furthermore, rich information of microseisms on wave development and propagation has a potential to proceed understanding of the extreme wave physics.

Exploration of Soliton Solutions to the Special Korteweg–De Vries Equation with a Stability Analysis and Modulation Instability

This work is concerned with Hirota bilinear, expa function, and Sardar sub-equation methods to find the breather-wave, 1-Soliton, 2-Soliton, three-wave, and new periodic-wave results and some exact solitons of the special (1 + 1)-dimensional Korteweg–de Vries (KdV) equation. The model of concern is a partial differential equation that is used as a mathematical model of waves on shallow water surfaces. The results are attained as well as verified by Mathematica and Maple softwares. Some of the obtained solutions are represented in three-dimensional (3-D) and contour plots through the Mathematica tool. A stability analysis is performed to verify that the results are precise as well as accurate. Modulation instability is also performed for the steady-state solutions to the governing equation. The solutions are useful for the development of corresponding equations. This work shows that the methods used are simple and fruitful for investigating the results for other nonlinear partial differential models.

Peculiarities of radio pulsars with long periods

The analysis of parameters of radio pulsars with periods P 5 sec has been carried out. It was found that there is not a clear dependence dP / dt on P on the diagram {dP / dt, P}. Such lack of any dependence can be explained in the frame of the disk model. It is shown that the pulse width decreases with increasing period for the sample considered. It is the opposite of the dependence in the generally accepted pulsar model. Such a behavior can be explained by the dependence of the level of radiation on the period, The alternative explanation is a non-dipole structure of magnetic field in the region of the generation of observed radiation. We consider the possibility of the description of extremely long intervals between successive pulses in pulsars J0901–4046 and J0250+5854 using the model of drift waves at the periphery of the magnetosphere. In the drift model rotation periods of these pulsars are several times shorter than the intervals between observed pulses.

Validation of an efficient two-layer non-hydrostatic wave model on a sloping foreshore

In the physical modelling of coastal engineering problems, use is often made of foreshores and transition slopes to obtain the desired wave conditions - both spectral parameters and wave height distribution - at a given location. Numerical wave models can be used to predict whether the target wave conditions are met for a given physical model layout and wave forcing. The XBeach non-hydrostatic two-layer model is a computationally efficient numerical model that has been validated for spectral wave parameters, but lacks validation of the simulated wave height distributions. In this work, wave flume data with high spatial density over a sloping foreshore is used to validate the ability of this numerical model to reproduce both spectral wave parameters and wave height distributions. As part of this effort, optimal settings have been derived for the wave breaking formulation used in the numerical model, resulting in recommended values for the maxbrsteep and reformsteep parameters of 0.40 and 0.20 respectively. From the results of the validation it is concluded that the numerical model is unsuccessful in reproducing the validation tests with 5.0% wave steepness, potentially due to the higher kph numbers on the generating model boundary. Hence, using the numerical model with values of kph ≥ 2 on the model boundary is not recommended. The XBeach non-hydrostatic two-layer model performs much better for the 1.0% and 2.5% wave steepness tests, where the spectral wave parameters are represented well. The corresponding wave height distributions are represented reasonably well up to the point that the relative water depth gets very shallow. For shallower water, the model is expected to underestimate the higher waves in the wave height distribution. Additionally, the numerical model is shown to reproduce the wave height distribution better than a commonly used analytical formulation for wave height distributions on slopes.

OPTIMIZATION OF THE SCATTERING MATRIX OF FREQUENCY -DETUNED ADD/DROP FILTERS FOR MULTIPLEXERS BUILT ON SYSTEMS OF OPTICAL DIELECTRIC RESONATORS WITH WHISPERING GALLERY MODES

Background. A significant increase in the speed of information transmission in fiber-optic communication networks is determined by the strict requirements imposed on the elemental base of receiving and transmitting devices. One of the important components of such devices is diplexers built on different notch and bandpass filters, which are often performed on dielectric resonators (DR) with whispering gallery mode (WGM) oscillations. Calculation and optimization of the parameters of multilink filters and diplexers built on DR is impossible without further development of the theory of their design. The development of the theory of diplexers today is often based on electrodynamic modelling, which is built on preliminary calculations of filter scattering parameters in various transmission lines with a complex topology of connections. Objective. The aim of this study is to construct electrodynamics' models of wave scattering on complex multi-connected DR structures with degenerate types of WGM natural oscillations, which contain several frequency-detuned bandpass or notch filters located in one or several transmission lines. To solve the scattering problem, we proposed a system of equations derived from perturbation theory for Maxwell's equations [24], modified to describe the DR fields with whispering gallery oscillations in transmission lines. The construction of such solutions is complicated by the fact that each of the partial optical resonators of the filters, in the case of excitation of azimuthally inhomogeneous WGM in it, has, as a rule, two degenerate types of natural oscillations. Moreover, each such type of oscillation is characterized by different complex values of the coupling coefficients with the line, open space, and also with other resonators. The latter circumstance leads to the fact that the systems of equations for the amplitudes of natural and forced oscillations of resonators are doubled. The signs of the coefficients of mutual coupling are usually different, this leads to the fact that the behaviour of DRs in the system becomes more difficult to predict, therefore the second objective of this work is to study the patterns of the scattering characteristics of line waves on systems of frequency-detuned DRs with degenerate types of oscillations with the possibility of constructing multiplexers for modern optical communication systems. Methods. The methods of technical electrodynamics are used for calculating and analysing scattering matrices. The end result is obtaining new analytical equations and formulas for new complex structures of coupled dielectric resonators with whispering gallery oscillations in the different transmission lines. Results. Frequency dependences of scattering matrices on complex structures of frequency-detuned filters built on coupled optical DR with whispering gallery oscillations located in one or more transmission lines are considered. Electromagnetic models of bandstop and add/drop filters are built, consisting of various optical resonators with degenerate types of natural oscillations. General analytical expressions of vector coefficients and matrices for building systems of equations describing coupled oscillations, as well as forced oscillations of resonators in cases of their use in optical filters with serial and parallel arrangement, are given. General solutions for the scattering field on frequency-detuned resonators located in different optical transmission lines have been found. Examples of calculating frequency dependences of the scattering matrix for the most interesting structures consisting of two different frequency-detuned filters are given. The frequency scattering characteristics of several types of devices are calculated, which consist of two notch filters with different blocking bands, made on detuned DRs in one transmission line. The possibilities of the earlier proposed method are demonstrated in the example of calculating the scattering characteristics of known types of diplexers built on the basis of the use of two add/drop filters with different frequency bandwidths. The frequency dependences of the scattering matrices of the two most common types of devices, located in parallel between two or four regular transmission lines of add/drop filters with different numbers of resonators; laterally coupled add/drop filters; parallel-coupled add/drop filters; twisted double-channel side-coupled integrated space sequence of resonators (SCISSORs), were studied. New scattering models of diplexers consisting of optical resonators of different connection topologies were built: serial, parallel with the use of laterally coupled add/drop filters; parallel-coupled add/drop filters; twisted double-channel SCISSORs. The frequency dependences scattering matrix of the diplexers were also calculated. The characteristics of the designed diplexers obtained from the examined filters of different types were compared. Conclusions. The theory of diplexer construction, which takes place on the simultaneous optimization of the scattering matrix of several filters built on complex systems of dielectric resonators with degenerate types of whispering gallery oscillations is expanded. A calculation method was developed and new analytical relations were found for the scattering matrix coefficients of optical diplexers of various types.

Electric circuit element boundary conditions for electromagneto-quasistatic and full wave models in A, φ potentials and their finite element implementation

Electric Circuit Element (ECE) boundary conditions (BC) defined for full-wave (FW) electromagnetic field allow a natural coupling between field devices and electric circuits. The novelty of this paper is that it shows how ECE BC can be implemented into a 3D-finite element method (FEM), when using A, a magnetic vector potential and φ, a scalar potential. Weak formulations are described and implemented in the free environment Open Numerical Engineering LABoratory(onelab). The validation is carried out on 3D examples solved both in frequency (FD) and time domain (TD), for FW formulations in potentials, as well as for corresponding Darwin approximations of Electromagneto-Quasistatic (EMQS) models. Results are compared with those obtained with a formulation in EV, where E is the electric field inside the domain and V is a scalar potential defined solely on the boundary. The results show that: 1) the use of potentials has some advantages over the EV formulation in TD only; 2) excitation type matters, the voltage excitation, here essential in FEM, proved to be the most robust one for the considered examples: a coplanar waveguide and a spiral inductor.

Investigation of electromagnetic wave propagation characteristics across various frequencies in porous media of goaf.

The reliable long-distance transmission of electromagnetic wave signals within goaf is fundamental for the implementation of wireless monitoring and early warning systems for goaf-related disasters. This paper establishes an experimental platform for electromagnetic wave signal transmission within goaf and develops a propagation model for electromagnetic waves in the porous media of goaf. The transmission characteristics of electromagnetic waves at various frequencies within the porous media environment of goaf are investigated through experimental and numerical simulation approaches. The results indicate that the received signal intensity of electromagnetic waves across different frequency bands diminishes with increasing propagation distance in the lossy environment of the goaf. Initially, the decay follows a logarithmic pattern, whereas, at later stages, the attenuation exhibits a gradual and smooth decrease. As the frequency increases, the initial attenuation amplitude of electromagnetic wave intensity rises; however, subsequent attenuation is largely unaffected by frequency, with the later attenuation rate being proportional to porosity. Electromagnetic waves at a frequency of 700 MHz exhibit a low attenuation coefficient under both experimental and simulated conditions, demonstrating superior stability and reliability. This frequency significantly enhances the overall performance of the communication system and is suitable for use as the operational frequency band in wireless sensor networks.

Differences in M‐components between triggered lightning striking the ground and overhead line

AbstractIn the summer of 2018–2019, rocket‐triggered lightning experiments were conducted in Guangzhou, China. There were two types of lightning targets: ground and overhead line. By comparing the current and the electric field data in the two cases, it was found that when the continuous current level (ICC) and current amplitude (IM) of M‐components (current pulses generated during the continuous current stage) are large, the time difference between the electric field peak and the current peak (TD) will always be small. The rise time (RT) and half peak width (THPW) of M‐components with high ICC and IM are low in both the cases. The threshold upper limit of TD in the case of lightning striking the ground is higher, approximately 2.6 times than that in the case of lightning striking the overhead line. We use an optimised guided wave model to simulate the electric field waveforms of M‐components. It was found that the shorter RT and THPW of the M‐component, the smaller TD. The changes in wave speed and IM cannot affect the size of TD, and the impact of distance changes is very weak. The difference in the threshold upper limit of TD may be related to the significant difference in ground impedance in two cases.

Solitons in the Fifth-Order KdV Equation with a Perturbation

Abstract The fifth-order KdV equation with a perturbation term is more consistent with the shallow water wave model in nature. By using the multi-scale perturbation expansion method, the leading-order asymptotic solution of the perturbed fifth-order KdV equation is derived. Furthermore, the asymptotic solution is reconsidered from the perspective of conservation laws, and consistent results are obtained. In addition, the numerical solution of the slowly varying solitary wave asymptotic solution is obtained by the Fourier spectral method under appropriate initial conditions to better understand its dynamic behavior. These results can enrich the research on fluid dynamics.

Estimating quasi-linear diffusion coefficients for varying values of density ratio

This paper considers a method for estimating bounce-averaged quasi-linear diffusion coefficients due to whistler-mode waves for a specified ratio of plasma frequency to gyrofrequency, ωp/Ωe, using values precomputed for a different value of that ratio. This approach was recently introduced to facilitate calculations associated with the “POES technique,” generalized to infer both wave intensity and cold plasma density from measurements of particle fluxes near the loss cone. The original derivation was justified on the basis of parallel-propagating waves but applied to calculations with much more general models of the waves. Here, we justify the estimates, which are based on equating resonant frequencies for differing values of ωp/Ωe and energy, for wide ranges of wave normal angle, resonance number, energy, and equatorial pitch angle. Refinements of the original estimates are obtained and tested numerically against full calculations of the diffusion coefficients for representative wave models. The estimated diffusion coefficients can be calculated rapidly and generally give useful estimates for energies in the 30-keV–300-keV range, especially when both relevant values of the ratio ωp/Ωe are large.

The Formation of Ion-Acoustic Solitary Waves in a Plasma Having Nonextensive Electrons and Positrons

In this plasma model, consisting of ions, electrons and positrons have been theoretically investigated when both the electrons and positrons are obeying q-nonextensive velocity distribution. The reductive perturbation method is used to obtain a Korteweg-de Vries(KdV) equation describing the basic set of normalized fluid equations. The ion-acoustic solitary waves model are depended on nonextensive parameter, electron to positron temperature ratio, ion to electron temperature ratio and streaming velocity are investigated numerically. It has been found that solely fast ion-acoustic modes can produce the coexistence of small amplitude rarefactive solitons.

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.