Model Wave Research Articles

Features of modeling of stress and strain waves in an anisotropic medium on the example of a wooden element

This article describes the hypotheses of the occurrence, propagation, and modification of stress and strain waves caused by external loads in isotropic and anisotropic infinite and finite elastic media. A model of an infinite elastic medium experiencing a point external impulse is presented. The model demonstrates the propagation of a longitudinal plane wave. Compaction and rarefaction of the medium are observed in the plane with wave propagation. A graph of changes in the amplitude of a longitudinal plane wave is presented in the same coordinate system. The problem is posed of expanding the numerical model of a finite elastic medium in the form of an anisotropic wooden rod experiencing a plane external impulse. The model should demonstrate the propagation of longitudinal and transverse waves and describe the volumetric deformation of an anisotropic material. Compaction and rarefaction of the medium are shown in the plane, coinciding with the direction of wave propagation. A graph of the change in the shear wave amplitude is presented in the same coordinate system. The combination of these two graphsreveals the difference in wave propagation velocities and the combination of amplitudes. The model will make it possible to identify the presence of Rayleigh waves and to describe the reflection of waves from the boundary of the medium.

Modeling of acoustoelastic borehole waves subjected to tectonic stress with formation anisotropy and borehole deviation

Sonic logging is a useful technique to estimate tectonic stress around a borehole. The key to successful evaluation of tectonic stress is having a thorough understanding of a forward model that generates responses of borehole waves to tectonic stress. We have developed a generic model to simulate responses of borehole waves to tectonic stress based on the semianalytical finite-element method and acoustoelasticity. This model can compute the distribution of tectonic stress around an inclined borehole with an arbitrary anisotropic formation and simulate the acoustoelasticities of borehole waves under this complicated stress. To avoid tedious and time-consuming code development, we also provide easy access to the model by reformulating and implementing the governing equations in a commercial software package. We validate the model by using three case studies in which analytical/numerical solutions are available, showing a good agreement between the results from our model and the solutions in the literature. We then apply the model to some important applications in boreholes, demonstrating that this model can provide a powerful tool for understanding the responses of borehole waves to tectonic stress.

Quality of the Wind Wave Forecast in the Black Sea Including Storm Wave Analysis

This paper presents the results of wind wave forecasts for the Black Sea. Three different versions utilized were utilized: the WAVEWATCH III model with GFS 0.25 forcing on a regular grid, the WAVEWATCH III model with COSMO-RU07 forcing on a regular grid, and the SWAN model with COSMO-RU07 forcing on an unstructured grid. AltiKa satellite altimeter data were used to assess the quality of wind and wave forecasts for the period from 1 April to 31 December 2017. Wave height and wind speed forecast data were obtained with a lead time of up to 72 h. The presented models provide an adequate forecast in terms of modern wave modeling (a correlation coefficient of 0.8–0.9 and an RMSE of 0.25–0.3 m) when all statistics were analyzed. A clear improvement in the wave forecast quality with the high-resolution wind forecast COSMO-RU07 was not registered. The bias error did not exceed 0.5 m in an SWH range from 0 to 3 m. However, the bias sharply increased to −2 or −3 m for an SWH range of 3–4 m. Wave forecast quality assessments were conducted for several storm cases.

Transformation of Water Wave Spectra into Time Series of Surface Elevation

Spectral wave modelling is widely used to simulate large-scale wind–wave processes due to its low computation cost and relatively simpler formulation, in comparison to phase-resolving or hydrodynamic models. However, some applications require a time-domain representation of sea waves. This article proposes a methodology to transform the wave spectrum into a time series of water surface elevation for applications that require a time-domain representation of ocean waves. The proposed method uses a generated phase spectrum and the inverse Fourier transform to turn the wave spectrum into a time series of water surface elevation. The consistency of the methodology is then verified. The results show that it is capable of correctly transforming the wave spectrum, and the significant wave height of the resulting time series is within 5% of that of the input spectrum.

Numerical Modeling of Failure Mechanisms in Articulated Concrete Block Mattress as a Sustainable Coastal Protection Structure

Shoreline protection remains a global priority. Typically, coastal areas are protected by armoring them with hard, non-native, and non-sustainable materials such as limestone. To increase the execution speed and environmental friendliness and reduce the weight of individual concrete blocks and reinforcements, concrete blocks can be designed and implemented as Articulated Concrete Block Mattress (ACB Mat). These structures act as an integral part and can be used as a revetment on the breakwater body or shoreline protection. Physical models are one of the key tools for estimating and investigating the phenomena in coastal structures. However, it does have limitations and obstacles; consequently, in this study, numerical modeling of waves on these structures has been utilized to simulate wave propagation on the breakwater, via Flow-3D software with VOF. Among the factors affecting the instability of ACB Mat are breaking waves as well as the shaking of the revetment and the displacement of the armor due to the uplift force resulting from the failure. The most important purpose of the present study is to investigate the ability of numerical Flow-3D model to simulate hydrodynamic parameters in coastal revetment. The run-up values of the waves on the concrete block armoring will multiply with increasing break parameter (0.5<ξm−1,0<3.3) due to the existence of plunging waves until it (Ru2%Hm0=1.6) reaches maximum. Hence, by increasing the breaker parameter and changing breaking waves (ξm−1,0>3.3) type to collapsing waves/surging waves, the trend of relative wave run-up changes on concrete block revetment increases gradually. By increasing the breaker index (surf similarity parameter) in the case of plunging waves (0.5<ξm−1,0<3.3), the low values on the relative wave run-down are greatly reduced. Additionally, in the transition region, the change of breaking waves from plunging waves to collapsing/surging (3.3<ξm−1,0<5.0), the relative run-down process occurs with less intensity.

The solar corona as an active medium for magnetoacoustic waves

The presence and interplay of continuous cooling and heating processes maintaining the corona of the Sun at the observed one million K temperature were recently understood to have crucial effects on the dynamics and stability of magnetoacoustic (MA) waves. These essentially compressive waves perturb the coronal thermal equilibrium, leading to the phenomenon of a wave-induced thermal misbalance (TM). Representing an additional natural mechanism for the exchange of energy between the plasma and the wave, TM makes the corona an active medium for MA waves, so that the wave can not only lose but also gain energy from the coronal heating source (similarly to burning gases, lasers and masers). We review recent achievements in this newly emerging research field, focussing on the effects that slow-mode MA waves experience as a back-reaction of this perturbed coronal thermal equilibrium. The new effects include enhanced frequency-dependent damping or amplification of slow waves, and effective, not associated with the coronal plasma non-uniformity, dispersion. We also discuss the possibility to probe the unknown coronal heating function by observations of slow waves and linear theory of thermal instabilities. The manifold of the new properties that slow waves acquire from a thermodynamically active nature of the solar corona indicate a clear need for accounting for the effects of combined coronal heating/cooling processes not only for traditional problems of the formation and evolution of prominences and coronal rain, but also for an adequate modelling and interpretation of magnetohydrodynamic waves.

A framework for automatically choosing the optimal parameters of finite-difference scheme in the acoustic wave modeling

An effective finite-difference (FD) scheme requires suitable FD parameters to ensure stability while having sufficient accuracy in the seismic modeling. The FD parameters such as time step, grid spacing and FD operator also affect the computational costs and storage requirements significantly. Thus, choosing the FD parameters should be the optimal trade-off between the stability, numerical accuracy and computational efficiency. However, the FD parameters usually be chosen through repeated manual tests, which is prone to unnecessary consumption. In this paper, we propose a framework for automatically choosing the FD parameters to achieve the optimal FD scheme in the acoustic wave modeling. Considering the computational efficiency, the proposed framework provides the maximum admissible time step under the stability condition. On the premise of the maximum time step, the proposed framework can find suitable parameters to ensure that the FD scheme has sufficient wavenumber bandwidth to deal with the maximum wavenumber or frequency of the wavefield. Dispersion and stability analyses prove that the FD parameters determined by our framework can effectively avoid dispersion errors while ensuring stability under the given conditions. Numerical experiments also prove the effectiveness of the framework in choosing FD parameters for the inhomogeneous velocity model. The framework can easily obtain the optimal FD parameters and can be recommended as a routine step for the FD methods.

Ultrasound-Enhanced Transcorneal Drug Delivery for Treatment of Fungal Keratitis.

Transcorneal drug delivery is hindered by ocular physical and biochemical properties, such as tear production, the epithelial layer of the cornea, and blinking. The aim of this study was to determine whether ultrasound can be applied to increase the transcorneal drug delivery of natamycin used in the treatment of fungal keratitis without dangerously overheating the surrounding ocular tissues. To verify the safety of various sets of ultrasound parameters, modeling studies were conducted using OnScale, an ultrasonic wave modeling software. Ultrasound parameters determined optimal for ocular tissue safety were used in a laboratory setting in a jacketed Franz diffusion cell setup. Histological images of the cross-section of the corneas used in experiments were examined for cell damage under a microscope. Increases in transcorneal drug delivery were seen in every treatment parameter combination when compared with the sham treatment. The highest increase was 4.0 times for 5 minutes of pulsed ultrasound at a 25% duty cycle and a frequency of 400 kHz and an intensity of 0.5 W/cm 2 with statistical significance ( P < 0.001). Histological analysis revealed structural damage only in the corneal epithelium, with most damage being at the epithelial surface. This study suggests that ultrasound is a safe, effective, and minimally invasive treatment method for enhancing the transcorneal drug delivery of natamycin. Further research is needed into the long-term effects of ultrasound parameters used in this study on human ocular tissues.

Modeling of nonlinear ion-acoustic solitary, snoidal and superperiodic wave phenomena due to ionospheric escape of Venus

Solar wind induces the escape of ions from the ionospheric shell of an unmagnetized planet, Venus. To analyze the dynamics of ions due to the escape process, the modeling of ion-acoustic waves (IAWs) is scrutinized for an interaction between an upper ionospheric plasma of Venus constituting mobile electrons with two kinds of positive ions, viz, H+ and O+ and the solar-wind which is composed of highly energized electrons and protons. The Sagdeev pseudopotential is examined for wave breaking phenomena. Employing the concept of phase plane analysis, the formulated autonomous dynamical systems are examined for all feasible nonlinear and supernonlinear periodic waves. To support the existence of nonlinear and supernonlinear waves, the graph of the total energy function is plotted in three-dimensional space. A typical set of Venusian plasma parameters are used to discuss the analytical solutions of the dynamical system by the method of Jacobi elliptic function. Effect of traveling wave velocity on the plot of the total energy function and the wave solutions are discussed.

Two-Dimensional Modeling of Three-Dimensional Waves

Two-Dimensional Modeling of Three-Dimensional Waves

Finite-difference modelling of 2-D wave propagation in the vicinity of dipping interfaces: a comparison of anti-aliasing and equivalent medium approaches

SUMMARY Finite-difference (FD) modelling of seismic waves in the vicinity of dipping interfaces gives rise to artefacts. Examples are phase and amplitude errors, as well as staircase diffractions. Such errors can be reduced in two general ways. In the first approach, the interface can be anti-aliased (i.e. with an anti-aliased step-function, or a lowpass filter). Alternatively, the interface may be replaced with an equivalent medium (i.e. using Schoenberg &amp; Muir (SM) calculus or orthorhombic averaging). We test these strategies in acoustic, elastic isotropic, and elastic anisotropic settings. Computed FD solutions are compared to analytical solutions. We find that in acoustic media, anti-aliasing methods lead to the smallest errors. Conversely, in elastic media, the SM calculus provides the best accuracy. The downside of the SM calculus is that it requires an anisotropic FD solver even to model an interface between two isotropic materials. As a result, the computational cost increases compared to when using isotropic FD solvers. However, since coarser grid spacings can be used to represent the dipping interfaces, the two effects (an expensive FD solver on a coarser FD grid) equal out. Hence, the SM calculus can provide an efficient means to reduce errors, also in elastic isotropic media.

Forward modeling of Rayleigh surface waves for analytical characterization of dominant dispersion trends

AbstractForward modeling is of critical importance for inversion analysis of surface wave methods to obtain shear‐wave velocity (VS) profiles of soil sites. The dynamic stiffness matrix (DSM) method can provide forward modeling of Rayleigh surface waves to simulate complex wave propagation in layered soil sites. However, contamination from body waves and interference of multiple Rayleigh wave modes can reduce the accuracy of theoretical dispersion curves, especially at irregular soil sites with embedded low‐velocity or high‐velocity layers. An analytical method is developed herein to combine the techniques of the multichannel analysis of surface waves method with the DSM method to improve the accuracy of the theoretical dispersion analysis for soil sites. The proposed method implements multichannel analysis of the analytical displacement responses to capture dominant dispersion trends. Comparison of the results obtained with the new method against those from the transfer matrix method and the literature indicates that the new method can (1) effectively minimize the effects of contamination caused by body waves and interference from several Rayleigh wave modes, and (2) generate accurate dominant dispersion trends for soil sites with various stiffness profiles, especially for the high‐frequency dispersion characteristics of the profiles with embedded low‐velocity layers.

A Theoretical Study of the N2 + H2 Reactive Collisions for High Vibrational and Translational Energies

High translational temperatures appear in the air inside the shock waves layers created by relatively large meteorites, reentry space vehicles, and hypersonic missiles. Under these conditions, reactions between molecular nitrogen and hydrogen are energetically permitted. In the present work, a quasiclassical trajectories study of the N2(v′)+H2(v″) reaction for relative translational energies covering the range of translational energy 20.0≤Etr/kcalmol−1≤120.0 is presented. In the calculations, several values of vibrational quantum numbers v′=0,4,6,8,10,12 and v″=4,6,8,10,12 have been considered. To model the interatomic interactions, a six-dimension global potential energy surface for the ground electronic state of N2H2 was used. The specific initial state reaction cross-sections and rate coefficients are reported. The energy effects produced by the reaction that could influence the shock wave modeling are here considered. An analysis of the possible impact of these processes under the atmospheric composition is also presented.

Numerical modeling of elastic waves using the random-enhanced QPSO algorithm

Numerical modeling of elastic waves using the random-enhanced QPSO algorithm

A fully nonlinear potential flow wave modelling procedure for simulations of offshore sea states with various wave breaking scenarios

An accurate representation of a given sea state is crucial for the study of hydrodynamic loads on offshore structures. It is straightforward to check the quality of the reproduced regular waves in a numerical wave tank (NWT). However, many more parameters need to be considered to ensure the quality of irregular waves. In this paper, a fully non-linear potential flow (FNPF) wave model is used to reproduce irregular sea states with different severity of wave breaking. The numerical model solves the velocity potential from the Laplace equation and the free surface boundary conditions using a finite difference method on a σ-coordinate grid. A comprehensive procedure is introduced to ensure the quality of the reproduced full-scale sea states. The effect of wave spectrum discretisation techniques and breaking wave algorithms are compared for an optimal performance. The evaluation of the simulation results takes into account the kurtosis and the wave crest distribution in addition to the wave spectra. The vertical arrangement of the σ-coordinate grid plays an important role in representing the dispersion relation and a grid optimisation method is explained. The current study provides a working procedure that reproduces high-fidelity irregular sea states with breaking waves in an efficient FNPF NWT.

Synthetic Modeling of Ambient Seismic Noise Tomography Data

Ambient seismic noise tomography is one of the most widely used methods in seismological studies today, especially after a comprehensive Earth noise model was published and noise analysis was performed on the IRIS Global Seismographic Network. Furthermore, the Power Spectral Density technique was introduced to identify background seismic noise in the United States. Many studies have been carried out using the ambient seismic noise tomography method which can be broadly grouped into several groups based on the objectives and research targets, such as to determine the structure of the earth’s crust and the upper mantle, to know the thickness of the sedimentary basins, to know the tectonic settings and geological structures, to know volcanic systems and geothermal systems, knowing near-surface geological features and as a monitoring effort the Ambient Noise Tomography method carried out by repeated measurements or time lapse. In this study, we investigate the characteristics of the ambient noise seismic tomography method, both its advantages and limitations of the method by utilizing synthetic data modeling using a simple geological model. Synthetic data is generated based on 1D dispersion curve forward modelling and the forward modeling of surface waves travel time for each period, which is then convoluted with the wavelets of each periods, then doing reverse correlation using a reference signal to produce synthetic recording data. We found that the estimate target depth and vertical resolution depend on the recorded data periods and the synthetic data modeling can be used as a basis in determining the acquisition design.

Acoustic response to transverse oscillations in a solar coronal loop

Context. Magnetohydrodynamic (MHD) waves play an important role in the dynamics and heating of the solar corona. Their investigation also reveals information about the local conditions. Transverse (Alfvénic) oscillations of loops commonly occur in response to solar eruptions. It has been shown that these oscillations elicit an acoustic response through wave coupling at the footpoint and the pondermotive force. Aims. We extend the modelling of wave coupling between a transverse loop oscillation and slow magnetoacoustic waves through line-tied footpoint boundary conditions by considering the effect of transverse loop structuring and non-linearity. Methods. We combine analytical wave modelling with fully non-linear MHD simulations to study the wave field of propagating slow waves in a two-dimensional slab loop (arcade) model. Results. We demonstrate that transverse loop oscillations generate propagating slow waves from the footpoints with the same periodicity but shorter wavelength determined by the local sound speed. The degree of wave coupling is proportional to the square root of the plasma-β. The slow wave field is anti-symmetric in the direction of transverse wave polarisation. We show through synthetic diagnostics that this has important consequences for their observability in terms of the orientation of the loop with respect to the observer. We also show that for the interpretation of intensity oscillations associated with typical loop oscillations the ponderomotive response also needs to be taken into account. The modelling presented here allows for the successful identification of the slow waves and pondermotive response in a previous observational study.

Performance evaluation of SWAN ST6 physics forced by ERA5 wind fields for wave prediction in an enclosed basin

In this study, the performance of SWAN (Simulating WAves Nearshore) spectral wave model ST6 physics forced by ERA5 reanalysis wind data were evaluated in predicting the wave properties in an enclosed basin, the Black Sea. ERA5 wind data were validated against in-situ measurements. Although two data match quite well, a 10–20% underestimation in wind speeds and velocity components was found. Spectral wave modeling study was conducted in two phases. In the first phase, 16 model setup combinations were generated using default parameterizations of SWAN spectral wave model with different physics (Westhuysen, Komen, Janssen, ST6) and with different wind sources (ERA5, ERA-Interim, and CFSv2). The model setups forced by ERA5 winds had the highest correlation values and in combination with ST6 physics performed better than the others in the prediction of wave heights. At the next stage, this model setup was calibrated at two stations by conducting 82 different parameterizations. Chosen model parameterization with overall satisfying performance was validated at five buoys. Comparisons among similar runtime model runs with timesteps up to 60 min and iteration steps up to four, show that higher timesteps with higher iterations give better results than lower time steps with one iteration. Debias and wind scaling parameters were found to be the most significant at adjusting wave heights. Comparison with previous calibration studies indicated that model runs based on calibrated ST6 physics parameterization and forced by ERA5 winds provided an increased accuracy of wave height predictions in the Black Sea.

Modeling of coastal infragravity waves using the spectral model WAVEWATCH Ⅲ

Forecasting coastal infragravity (IG) waves is crucial in preventing coastal disasters caused by IG waves. In this study, the performance of the unstructured WAVEWATCH Ⅲ (WW3) in predicting coastal IG waves is comparatively assessed using in-situ wave measurements, considering the effects of numerical schemes, time steps, and IG-source parameterization methods. The wave measurements are performed using three acoustic sensors installed at the coast of south Sri Lanka, with two being near or inside a harbor.Sensitivity analysis of the numerical schemes and time steps shows that the explicit scheme combined with a small time step leads to unexpected oscillations of the IG wave height. However, the time step has a negligible influence on the performance of the implicit scheme combined with the domain decomposition method. Generally, IG sources estimated from the empirical formula method (source M1) and the second-order spectrum method (source M2) perform similarly in reproducing the IG wave height. Regarding the IG frequency spectrum, both the IG sources properly predict the magnitude of the spectral density, but the spectral shapes are not adequately captured. M2 may provide a better directional spread of the IG wave energy. Attention is also paid to the IG waves inside the harbor. The IG waves within the harbor are underestimated, owing to the lack of some mechanisms related to IG waves in the simulation. M1 should be adopted when crudely predicting the magnitude of IG waves inside a harbor. Overall, the unstructured WW3 can effectively predict the coastal IG wave height in southern Sri Lanka, with significant correlation and acceptable errors, when compared with in-situ measurements. Finally, the IG source M1 is refined to remove the erroneous spectral gap between the IG and wind-wave frequency bands in the WW3 spectra when compared to the in-situ observed spectra.

Overcoming excessive numerical dissipation in SPH modeling of water waves

Excessive nonphysical energy dissipation is a problem in Smoothed Particle Hydrodynamics (SPH) when modeling free surface waves, resulting in a significant decrease in wave amplitude within a few wavelengths for progressive waves. This dissipation poses a limitation to the physical scale of SPH applications involving water wave propagation. Some prior solutions to this wave decay problem rely on elaborate schemes, which require a complex, or non-straightforward, implementation. Other approaches demand large smoothing lengths that lead to longer simulation times and potential degradation of the results. In this work we present an approach based on a kernel gradient correction. Our scheme is fully 3D and solves the main known drawbacks of kernel gradient corrections, such as instabilities and lack of momentum conservation. The latter is ensured by adopting an averaged correction matrix, so as to conserve reciprocity during particle interactions. We test our model with a standing wave in a basin and a progressive wave train in a wave tank, and in both cases no nonphysical decay occurs. A comparison to an approach based on large smoothing factors shows advantages both in quality of the results and simulation time.