Wave Propagation Research Articles

Rainbow trapping of out-of-plane mechanical waves in spatially variant beam lattices

We numerically and experimentally investigate the propagation of mechanical waves in two-dimensional periodic and spatially graded elastic beam lattices. Experiments on metallic lattices admit the characterization of the linear elastic wave dispersion over a wide range of frequencies, resulting in complete, experimentally-constructed dispersion surfaces in excellent agreement with predictions obtained from finite element-based Bloch wave analysis. While Timoshenko beam theory is shown to be sufficiently accurate for predicting the lowest modes, experiments prove that solid finite elements are required to capture the dispersion relations at higher frequencies as well as when mode coupling occurs. Based on an improved numerical procedure, group velocity maps further highlight the directionality of wave dispersion and allow for the simple identification of bandgaps. In addition to classically studied periodic trusses, we extend the framework to spatially graded structures and demonstrate acoustic rainbow trapping in beam lattices undergoing out-of-plane vibrations. Our experiments confirm broadband vibration attenuation of the typical meta-wedge type previously observed only in optics and few mechanical studies. Results further show convincing agreement between Bloch theory-based predictions, finite element simulations, and experimental measurements. Such spatially-variant architected lattices show great promise for steering the motion of elastic waves in applications from wave guiding and wave shielding to energy harvesting.

Ultrasonic wave characteristics in multiscale cementitious materials at different stages of hydration

Monitoring the microstructural change in cementitious materials during hydration is an essential but challenging task. Therefore, a non-invasive and sophisticated technique is warranted to understand the microscopic behaviour of the multiphase cementitious materials (where the length scale of the constituents varies from centimeters to micrometers) in different stages of hydration. Due to exothermic hydration reactions, different hydration products start to evolve with individual mechanical properties. In concrete, an interface transition zone (ITZ) appears between the aggregate surface and paste matrix, which influences the overall properties of concrete material. In the present research, 1) several wave characteristics, such as wave velocity, energy distribution, and signal phase are found out using Ultrasonic Pulse Velocity (UPV), Wavelet Packet Energy (WPE) and Hilbert Transform (HT) methods, to monitor the hydration mechanism (1d-28d) in cement-based materials with two levels of heterogeneities (cement paste and concrete, representing microscale and mesoscale, respectively). Also, the unique nonlinear behaviour is studied in the frequency domain using the promising Sideband Energy Ratio (SER) and Sideband Peak Count Index (SPC-I) methods. 2) Numerical simulations are carried out to understand the wave interaction in the developing microstructure. A discretized microstructure of cement shows microscopic details of each phase at any instant of hydration (e.g., formation stage and after complete maturity level). The experimental and numerical investigations on the characteristics of the nonlinear ultrasonic wave propagation show the impact of microstructural development of multi-scale cementitious materials during hydration.

Wave propagation over a non-reflective profile of limited depth

Non-reflective wave propagation is of great importance for applications because it allows energy to be transmitted over long distances. The paper discusses the method of reducing the equations of the linear theory of shallow water to a wave equation with a variable coefficient in the form of an inverse hyperbolic sine, the solution of which is represented as a composition of traveling waves. Thanks to this, a new non-reflective bottom profile has been obtained, which reaches a constant at infinity. Wave behavior on the shore is discussed, as well as the conditions under which the wave field remains finite on it. A detailed analysis of the obtained exact solution to the shallow water equations is given in the paper.

Effect of low blockage ratio obstacle on explosion characteristic in methane/air mixture

Methane/air explosion is one of the common hazards in process and mining industries. In this study, the methane explosion propagation is studied, and two-dimensional configuration is considered. The gas phase equations are solved using an OpenFOAM code for compressible reacting flow, EXiFOAM. The effects of the low blockage ratio (LBR) obstacles are investigated. The results show that the flame propagation speed, flame structure, shock wave propagation, and gas flow are considerably affected by LBR obstacles. Specifically, the flame propagation speed first increases and then decreases. As the initial pressure increases, the flame propagation speed gradually increases. The maximum speed is up to 500 m/s, when the initial pressure is 1.5 MPa. If the flame propagation is prevented, resulting in the flame deformation. Moreover, the flame disruptive phenomenon is captured due to the reflected waves. In front of the obstacle, the cellular structures of the high-pressure distribution are formed. Note that the tiny cellular structures are produced in the wake of the leading shock. Furthermore, a high-speed flow region and two low-speed flow regions are produced around the LBR obstacles. It is found that as the initial pressure increases, the explosion pressure is larger, while the temperature change is not obvious. These research findings have implications for enhancing safety production in coal mines.

Analyzing bifurcation, stability, and wave solutions in nonlinear telecommunications models using transmission lines, Hamiltonian and Jacobian techniques

This study presents a comprehensive analysis of a nonlinear telecommunications model, exploring bifurcation, stability, and wave solutions using Hamiltonian and Jacobian techniques. The investigation begins with a thorough examination of bifurcation behavior, identifying critical points and their stability characteristics, leading to the discovery of diverse bifurcation scenarios. The stability of critical points is further assessed through graphical and numerical methods, highlighting the sensitivity to parameter variations. The study delves into the derivation of both numerical and analytical wave solutions, aligning them with energy orbits depicted in phase portraits, revealing a spectrum of wave behaviors. Additionally, the analysis extends to traveling wave solutions, providing insights into wave propagation dynamics. Notably, the study underscores the efficacy of the planar dynamical approach in capturing system behavior in harmony with phase portrait orbits. The findings have significant implications for telecommunications engineers and researchers, offering insights into system behavior, stability, and signal propagation, ultimately advancing our understanding of complex nonlinear dynamics in telecommunications networks.

Waves in space-dependent and time-dependent materials: A systematic comparison

Waves in space-dependent and in time-dependent materials obey similar wave equations, with interchanged time- and space-coordinates. However, since the causality conditions are the same in both types of material (i.e., without interchangement of time- and space-coordinates), the solutions are dissimilar.We present a systematic treatment of wave propagation and scattering in 1D space-dependent and in 1D time-dependent materials. After formulating unified equations, we discuss Green’s functions and simple wave field representations for both types of material. Next we discuss propagation invariants, i.e., quantities that are independent of the space coordinate in a space-dependent material (such as the net power-flux density) or of the time coordinate in a time-dependent material (such as the net field-momentum density). A discussion of general reciprocity theorems leads to the well-known source–receiver reciprocity relation for the Green’s function of a space-dependent material and a new source–receiver reciprocity relation for the Green’s function of a time-dependent material. A discussion of general wave field representations leads to the well-known expression for Green’s function retrieval from the correlation of passive measurements in a space-dependent material and a new expression for Green’s function retrieval in a time-dependent material.After an introduction of a matrix–vector wave equation, we discuss propagator matrices for both types of material. Since the initial condition for a propagator matrix in a time-dependent material follows from the boundary condition for a propagator matrix in a space-dependent material by interchanging the time- and space-coordinates, the propagator matrices for both types of material are interrelated in the same way. This also applies to representations and reciprocity theorems involving propagator matrices, and to Marchenko-type focusing functions.

Investigating pseudo parabolic dynamics through phase portraits, sensitivity, chaos and soliton behavior

This research examines pseudoparabolic nonlinear Oskolkov-Benjamin-Bona-Mahony-Burgers (OBBMB) equation, widely applicable in fields like optical fiber, soil consolidation, thermodynamics, nonlinear networks, wave propagation, and fluid flow in rock discontinuities. Wave transformation and the generalized Kudryashov method is utilized to derive ordinary differential equations (ODE) and obtain analytical solutions, including bright, anti-kink, dark, and kink solitons. The system of ODE, has been then examined by means of bifurcation analysis at the equilibrium points taking parameter variation into account. Furthermore, in order to get insight into the influence of some external force perturbation theory has been employed. For this purpose, a variety of chaos detecting techniques, for instance poincaré diagram, time series profile, 3D phase portraits, multistability investigation, lyapounov exponents and bifurcation diagram are implemented to identify the quasi periodic and chaotic motions of the perturbed dynamical model. These techniques enabled to analyze how perturbed dynamical system behaves chaotically and departs from regular patterns. Moreover, it is observed that the underlying model is quite sensitivity, as it changing dramatically even with slight changes to the initial condition. The findings are intriguing, novel and theoretically useful in mathematical and physical models. These provide a valuable mechanism to scientists and researchers to investigate how these perturbations influence the system’s behavior and the extent to which it deviates from the unperturbed case.

Rough bed hydrodynamics under wave-current interactional flow field: double averaging approach

ABSTRACT The effect of surface wave on the double-averaged (DA) current-only flow properties is examined over two different types of rough beds comprising hemispherical elements with regular and staggered arrangements. For each case, the relative roughness spacing of p/r = 4 is maintained, where p = pitch distance and r = hemisphere height. The changes in turbulence characteristics against the water depth are analysed for superimposed surface waves propagating along the current with 1 and 2 Hz frequencies. The effect of regular and staggered roughness arrangements on different turbulence characteristics is explored. Results demonstrate that the DA stream-wise velocity decreases and increases at the outer region and within the roughness region, respectively, due to wave propagation. Owing to the surface wave, the DA intensity and form-induced intensity increase above the roughness layer and decrease within the bottom boundary layer. The values of form-induced intensities are smaller (greater) than the DA turbulence intensities at each considered flow depth within the roughness (outer) layer. For the entire flow depth, the values of DA Reynolds stress decrease due to wave interactions along a steady current. Again, the turbulence is observed to be close to isotropic for the current-only flow at the outer zone, while the flow transits to an anisotropic state with wave imposition on current. Further, the computed values of the turbulence indicator and dispersion functions are used for the identification of the level of turbulence and dispersion at each flow depth for the locations upstream and downstream of a hemisphere in the hemispherical bed.

On traveling wave solutions with stability and phase plane analysis for the modified Benjamin-Bona-Mahony equation.

The modified Benjamin-Bona-Mahony (mBBM) model is utilized in the optical illusion field to describe the propagation of long waves in a nonlinear dispersive medium during a visual illusion (Khater 2021). This article investigates the mBBM equation through the utilization of the rational [Formula: see text]-expansion technique to derive new analytical wave solutions. The analytical solutions we have obtained comprise hyperbolic, trigonometric, and rational functions. Some of these exact solutions closely align with previously published results in specific cases, affirming the validity of our other solutions. To provide insights into diverse wave propagation characteristics, we have conducted an in-depth analysis of these solutions using 2D, 3D, and density plots. We also investigated the effects of various parameters on the characteristics of the obtained wave solutions of the model. Moreover, we employed the techniques of linear stability to perform stability analysis of the considered model. Additionally, we have explored the stability of the associated dynamical system through the application of phase plane theory. This study also demonstrates the efficacy and capabilities of the rational [Formula: see text]-expansion approach in analyzing and extracting soliton solutions from nonlinear partial differential equations.

Understanding Ultrasonic Wave Behavior in Liquid Media: A Comprehensive Overview

To comprehensively understand molecular processes, it is essential to analyze how thermodynamic parameters change with temperature and composition, providing valuable insights into molecular interactions. The industry's demand for precise information on the physical and chemical characteristics of different liquid combinations underscores the importance of such research. Researchers employ an ultrasonic interferometer for measuring ultrasonic wave velocity, a specific gravity bottle for liquid density determination, and an Ostwald viscometer for viscosity measurements. The propagation of ultrasonic waves can affect the physical properties of a medium, providing insights into the physics of liquids and solutions. Research has explored how frequency and temperature can impact thermoacoustic characteristics. Scientists have identified the nature of the forces between molecules, including hydrogen bonds, charge transfer complexes, and the breaking and formation of such bonds through their investigations. By measuring ultrasonic wave velocity, liquid density, and viscosity, researchers can analyze a range of acoustic and thermodynamic properties, thus significantly advancing our understanding of molecular interactions within each sample. Additionally, a comprehensive explanation of the measured parameters is provided to offer detailed insights into the studied phenomena, enhancing the overall understanding of molecular processes in liquid mixtures.

Defect detection within filling layer of subway slab ballastless track based on impulse response method

The impulse response method, as a mechanical impedance analysis method with high-impact energy, can provide a rapid assessment of structural integrity. For this reason, the impulse response method is applied to subway slab ballastless tracks, and the theory behind this method, as well as the applicability of detecting the voids within the self-compacting concrete (SCC) filling layer, are deeply studied. The theoretical derivation of the mobility function of subway slab ballastless track under impact load is performed. The finite element model is established and the propagation of elastic waves in the process of impulse response method is simulated. The study also investigates the sensitivity of various characteristic parameters and the frequency analysis range to void identification in the SCC filling layer. Furthermore, the characteristic parameters for defect identification in the SCC filling layer are constructed and subsequently validated through a full-scale test. The results reveal that the impulse response method is capable of generating elastic waves with higher energy and longer wavelengths within the structure. This characteristic is advantageous for the detection of concealed defects in the multi-layer structure. The mobility spectrum of subway slab ballastless track exhibits multi-frequency peak characteristics, and the calculated cut-off frequency of the peak-mean mobility ratio should be extended to more than 1600 Hz. Among the three characteristic parameters of peak mobility, dynamic stiffness, and peak-mean mobility ratio, the peak-mean mobility ratio has the advantage of accurately identifying the void position and providing a more precise range.

Improvement of linearity in trap-rich substrates for radio frequency applications: Which of donor and acceptor trap is the best?

This paper investigates the effect of volume traps intentionally introduced into a silicon-on-insulator (SOI) substrate by inserting a layer of polysilicon beneath buried oxide. In radio frequency applications, this type of substrate, referred to as trap-rich, is known to considerably reduce the generation of harmonics resulting from the parasitic non-linear charge dynamics introduced by the substrate handler under the buried oxide. This analysis focuses on a test vehicle in the form of an integrated coplanar waveguide on two types of substrates, namely, high-resistivity SOI substrates with and without a trap-rich layer. From a modeling point of view, a simulation methodology is implemented in order to convert the 3D simulation of the coplanar waveguide into a 2D treatment that takes into account the wave propagation effect associated with the distributed nature of the transmission line. As a first step, this modeling strategy is implemented to reproduce the effect of increasing substrate resistivity on 2nd and 3rd harmonic reductions, leading to an excellent agreement with experimental data. Building on this validation of the simulation method, we have opted to simulate the non-linear response of the transmission line on the SOI trap-rich substrate by simplifying the trap distribution model. To avoid the adoption of unverified and strongly process-dependent trap distributions across the bandgap, a midgap monovalent trap density has been introduced, either acceptor or donor density. A monovalent density of acceptor traps with a concentration of 1016 cm−3 and a carrier lifetime of 0.1 ns has been shown to reproduce the experimental data very accurately with a substantial reduction in 2nd and 3rd harmonics. A detailed analysis of the displacement current waveforms explains the beneficial role of acceptor traps compared with donor traps.

An imaging condition for acoustic reverse time migration with implicit angle‐dependent weighting factors and its extended applications for imaging elastic P–P and S–S data

AbstractThe imaging condition is a crucial component of the reverse time migration. In its conventional form, it involves cross‐correlating the extrapolated source‐ and receiver‐side wavefields. Effective imaging conditions are usually developed to suppress imaging artefacts (e.g. low‐wavenumber artefacts) and enhance the image quality. For acoustic reverse time migration, not only the scalar pressure but also their spatial and/or time derivatives are used in the imaging condition, similar to the gradient terms of adjoint tomography. These operations implicitly introduce additional angle‐domain weighting factors to the image results. In this study, based on an analysis of angle‐dependent properties of the existing imaging conditions, we propose a new imaging condition tailored for acoustic reverse time migration. It can be implemented efficiently using the variables within the finite‐difference solver. Without explicitly measuring wave propagation directions, the proposed imaging condition can naturally suppress the low‐wavenumber artefacts while maintaining a relatively wider imaging aperture, thereby corresponding to a broader wavenumber sampling range. Additionally, the evolved imaging conditions for imaging elastic P–P and S–S scattering and reflections are also formulated. In the angle domain, we conduct a comparative analysis between existing imaging conditions and the newly proposed ones. Various numerical examples are provided to demonstrate the advantages of the new imaging conditions. A comprehensive understanding of their angle‐domain properties may be further beneficial to constructing reasonable inversion strategies for full waveform inversion.

Nonclassical wave propagation measurements in the high temperature vapor of D6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {D}_{6}$$\\end{document} with the asymmetric shock tube for experiments in rarefaction waves (ASTER)

A novel test setup called the asymmetric shock tube for experiments on nonideal rarefaction waves (ASTER) has been commissioned at Delft University of Technology. The ASTER, which works according to the principle of Ludwieg tubes, is designed to generate and measure the speed of small and finite amplitude waves propagating in the dense vapors of fluids formed by complex organic molecules, therefore in the nonideal compressible fluid dynamics regime. The ultimate goal of the associated research is to prove the existence of nonclassical gasdynamics. The setup consists of a high-pressure charge tube and a vacuum tank separated by a glass disk equipped with a breaking mechanism for rarefaction waves experiments. When the glass disk is broken, an expansion wave propagates into the tube in the direction opposite to the fluid flow. The propagation speed of this wave is measured using a time-of-flight method with the help of four fast-response pressure sensors placed equidistantly in the middle of the tube. The charge tube can withstand pressures and temperatures of up to 15 bar and 400∘C\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{\\circ }\\mathrm{C}$$\\end{document}. Preliminary rarefaction experiments were successfully conducted using dodecamethylcyclohexasiloxane, D6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {D}_{6}$$\\end{document}, as the working fluid and at pressures and temperatures of up to 9.4 bar and 372∘C\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{\\circ }\\mathrm{C}$$\\end{document} , respectively. The results of an experiment featuring the initial state for which a theoretical model predicts the nonclassical acceleration of rarefaction waves show that the propagation is qualitatively different from that put into evidence by experiments for which the propagation is classic. Upcoming setup improvements and experimental campaigns are planned with the objective of experimentally verifying the existence of nonclassical gasdynamics.Graphical abstract

Variability and Dynamics of the Kuroshio and Mindanao Current during the 2010/11 La Niña and in Late 2012

Abstract Variability of two Pacific western boundary currents (WBCs)—the Kuroshio and the Mindanao Current—during the strong 2010/11 La Niña event is investigated using ship-based hydrographic observations and moored current-meter data collected off the east coasts of the Philippines. The geostrophic currents calculated using the hydrographic data show that, during the 2010/11 La Niña winter, the Kuroshio decreased by ∼10 Sv (1 Sv ≡ 106 m3 s−1), whereas the Mindanao Current increased by ∼5–10 Sv, relative to the normal winter in late 2012. The interannual variability based on the hydrographic data is confirmed by moored current-meter measurements and satellite altimeter geostrophic currents. A coastally trapped Kelvin wave model is used to explain the interannual variability of the two WBCs during the different ENSO phases. The good comparison of the simulated sea level anomalies around the Philippines with the altimeter data suggests that the interannual variability of the WBCs is associated with Kelvin wave propagation from the Sulawesi–Sulu Seas clockwise around the Philippine Archipelago. We identified that the Kelvin waves are excited by downwelling equatorial Rossby waves propagating into the Indonesian Seas during the La Niña. The transport anomalies of the WBCs are comparable to the total meridional transport anomalies integrated across the interior North Pacific Ocean, suggesting the importance of the WBCs in the heat charge–discharge processes of the western Pacific warm pool during ENSO events. Significance Statement The two western boundary currents (WBCs)—the Kuroshio and the Mindanao Current—play the role of closing the subtropical and tropical gyre circulation of the Pacific Ocean. Their variability during ENSO is unknown. Existing studies based on numerical modeling suggest that their variability is highly correlated with ENSO, with the Kuroshio stronger and Mindanao Current weaker during La Niña and vice versa during El Niño. Here, we use in situ hydrographic observations combined with mooring and satellite altimeter data to show that the Kuroshio transport decreases and the Mindanao Current transport increases during the 2010/11 La Niña, the dynamics of which are controlled by the Kelvin wave propagation from the Sulawesi–Sulu Seas clockwise around the Philippine Archipelago. The result is important for the warm pool dynamics during ENSO.

A cell-centered implicit finite difference scheme to study wave propagation in acoustic media: A numerical modeling

In the present paper, we present a Cell-Centered Implicit Finite Difference (CCIFD) operator-based numerical scheme for the propagation of acoustic waves that is very effective, accurate, and small in size. This scheme requires fewer estimation points than the traditional central difference derivative operator. Any numerical simulation is significantly impacted by the precision of a numerical derivative. Long stencils can deliver excellent accuracy while also minimizing numerical anisotropy error. However, a long stencil requires a lot of computational resources, and as these derivatives get bigger, they could start to look physically unrealistic due to contributions from nodes located extremely far, wherein the derivative is local in nature. Furthermore, using such lengthy stencils at boundary nodes may result in errors. The present article investigates a cell-centered fourth order finite difference scheme to model acoustic wave propagation which utilizes a lesser number of nodes in comparison to the traditional Central Difference (CD) operator. However, in general the implicit derivative operator has high computational cost and therefore despite its significant advantages it is generally avoided to be implemented in applications. This serves as a motivation for the present paper to explore a technique called CCIFD that significantly decreases the computational expense by nearly fifty percent. Additionally, spectral characterization of the CCIFD derivative operator has been analyzed and discussed. Finally, the wave propagation has been numerically simulated in 2-dimensional homogeneous and Marmousi model using CCIFD scheme to validate the applicability and stability of the scheme.

MS-GWaM: A Three-Dimensional Transient Gravity Wave Parametrization for Atmospheric Models

Abstract Parameterizations for internal gravity waves in atmospheric models are traditionally subject to a number of simplifications. Most notably, they rely on both neglecting wave propagation and advection in the horizontal direction (single-column assumption) and an instantaneous balance in the vertical direction (steady-state assumption). While these simplifications are well justified to cover some essential dynamic effects and keep the computational effort small, it has been shown that both mechanisms are potentially significant. In particular, the recently introduced Multiscale Gravity Wave Model (MS-GWaM) successfully applied ray-tracing methods in a novel type of transient but columnar internal gravity wave parameterization (MS-GWaM-1D). We extend this concept to a three-dimensional version of the parameterization (MS-GWaM-3D) to simulate subgrid-scale nonorographic internal gravity waves. The resulting global wave model—implemented into the weather forecast and climate code Icosahedral Nonhydrostatic (ICON)—contains three-dimensional transient propagation with accurate flux calculations, a latitude-dependent background source, and convectively generated waves. MS-GWaM-3D helps reproduce expected temperature and wind patterns in the mesopause region in the climatological zonal mean state and thus proves a viable internal gravity wave (IGW) parameterization. Analyzing the global wave action budget, we find that horizontal wave propagation is as important as vertical wave propagation. The corresponding wave refraction includes previously missing but well-known effects such as wave refraction into the polar jet streams. On a global scale, three-dimensional wave refraction leads to a horizontal flow-dependent redistribution of waves such that the structures of the zonal mean wave drag and consequently the zonal mean winds are modified.

Experimental study on the influence of water depth and bed slope variations on dam-break flood wave propagation

Damage to dam structures frequently results in catastrophic consequences. Consequently, understanding of the characteristics of the movement of dam-break flow along the sloping wet bed can assist in the issuance of timely flood warnings and risk mitigation. In this study, a series of large-scale flume experiments was conducted with the objective of investigating the effects of upstream and downstream water depth and bed slope on the propagation of dam-break waves. The water level is measured and processed to calculate the wavefront velocity. Results show that the wave propagation behavior can be classified as bore and undular waves through the global Froude numbers (Frx) and local Froude numbers (Frl). When Frx < 1.225 or Frl < 1.475, the dam-break wave propagates as the undular wave. In the undular wave state, the wavefront velocity (U) decreases with increasing water depth ratio α. Additionally, the U with Frx shows a similar trend, where the experimental value surpasses the analytical solution. The dimensionless maximum wave height (ΔHmax) increases with Frx and then decreases. The deviation from the analytical solution ranges between 67.22% and 127.38%. When Frx > 1.225 or Frl > 1.475, the dam-break wave propagates as the bore wave. In the bore wave state, the U increases slightly with the water depth ratio α, while the change rule of U with Frx is similar to it. The dimensionless maximum wave height (ΔHmax) remains relatively constant as Frx increases, showing a high degree of consistency with the analytical solution. The presence of bed slope results in increased wavefront velocity and wave heights, while an increase in α results in the emergence of more pronounced undular wave phenomena. Furthermore, the experimental results are compared with existing analytical solutions, and the validity of the analytical solutions and their limitations are discussed.

Nonlinear propagation of ion-acoustic waves along with their bifurcation analysis in a negative ion plasma in the presence of quartic nonlinearity

In this article, the propagation of ion-acoustic shock and periodic waves along with their dynamical analysis around the supercritical values is studied in a (1 + 1)-dimensional collisionless negative ions plasma system comprising of inertia SF 6− with mass m−i and temperature T−i, inertia K+ with mass m+i and temperature T+i and inertialess non-extensive distributed electrons. By considering the appropriate starching coordinates and expansion of perturbation quantities, the Burgers-type equation with quartic nonlinearity is derived. Using the traveling wave transformation, a planar dynamical system is formed. The phase portrait is drawn and the associated nonlinear waves are analyzed. The research presented could be beneficial for understanding and forecasting localized electrostatic disturbances in the F- and D-layers of Earth's ionosphere as well as for guiding future experimental investigations in plasma laboratories.

Investigating the Intense Sediment Load by Dam‐Break Floods Using a Meshless Two‐Phase Mathematical Model

AbstractExtreme precipitation is increasing the risk of dam breaks and formation occurring debris dams. Accurate prediction of dam‐break wave propagation is critical to disaster emergency management. Intense bed‐load transport by dam‐break floods can result in a dramatic change of topography, which in turn may affect flood propagation. However, only a very few studies have investigated the thin intense bed‐load layer under dam‐break floods. In this paper, a meshless two‐phase mathematical model is utilized to examine the water velocity, sediment velocity and volumetric fraction, and bed‐load transport flux as well as energy dissipation in bed‐load layer. The model is applied to simulate two‐ and three‐dimensional laboratory experiments of dam‐break wave over erodible beds. For the two‐dimensional experiment, the relative root mean square errors in computed water surface are all below 3.60% and those in profiles of bed‐load layer and static bed are mostly below 13.40%. For the three‐dimensional case, the relative error in computed highest water level is lower than 5.9%. Sediment stream‐wise velocity in bed‐load layer follows a power‐law vertical distribution while sediment volumetric fraction decreases linearly upwards. Accordingly, a formulation of the vertical distribution of bed‐load transport flux, contradictory to the parabolic law in existing studies, is proposed. Most of the water mechanical energy transferred to the sediment is dissipated due to the shear stress in the intense bed‐load layer while only a limit part is kept by the sediment grains. Energy dissipation due to sediment shear stress dominates the consumption of total mechanical energy in the two‐phase system.