Decay Of Waves Research Articles

Lie symmetry method to discuss the optimal system of Lie subalgebras and similarity solutions for shock propagation in a perfectly conducting dusty gas with magnetic field in rotating medium

In this paper, the similarity solutions for the shock wave propagation in a perfectly conducting dusty gas under the effect of axial or azimuthal magnetic field in the case of rotating medium by using Lie symmetry method have been discussed. The optimal system of one-dimensional Lie subalgebras related to the hyperbolic system of nonlinear partial differential equations had been constructed by using general invariant function and general adjoint transformation matrix. The optimal system is the collection of inequivalent optimal classes, which provides crucial information regarding different types of the similarity solutions. On the basis of the optimal system, we have discussed all possible similarity solutions for inequivalent optimal classes individually. Also, we have found that the similarity solutions exist in two cases for power law shock path and in one case with exponential law shock path. The shock wave decay is due to an increment in the physical parameter such as shock Cowling number or non-idealness parameter or adiabatic exponent or rotational parameter. For smaller value of the ratio of density of solid particles to initial species density of the gas i.e. [Formula: see text], the shock strength decreases with an increment in the mass fraction of solid particles in the mixture [Formula: see text], but the shock strength decreases as [Formula: see text] increases for [Formula: see text]. Also, the shock strength increases with an increment in [Formula: see text] at constant [Formula: see text]. It is observed that the shock wave is stronger in the presence of axial magnetic field as compared to azimuthal magnetic field.

Kinetic mixing, proton decay and gravitational waves in SO(10)

We present an SO(10) model in which a dimension five operator induces kinetic mixing at the GUT scale between the abelian subgroups U(1)B−L and U(1)R. We discuss in this framework gauge coupling unification and proton decay, as well as the appearance of superheavy quasistable strings with Gμ ~ 10−8 – 10−5, where μ denotes the dimensionless string tension parameter. We use Bayesian analysis to show that for Gμ values ~ 4 × 10−7 − 10−5, the gravitational wave spectrum emitted from the quasistable strings is in good agreement with the recent pulsar timing array data. Corresponding to Gμ values ~ 10−8 − 2 × 10−7, proton decay is expected to occur at a rate accessible in the Hyper-Kamiokande experiment. Finally, we present the gravitational wave spectrum emitted by effectively stable strings with Gμ ≈ 10−8 that have experienced a certain amount of inflation. This can be tested with future detectors in the μHz frequency range.

Energetic seed particles in self-consistent particle acceleration modeling at interplanetary shock waves

Aims. The study investigates the relevance of the seed particle population in the results of particle acceleration in interplanetary shock waves, when wave–particle interactions are treated self-consistently. Methods. We employed the SOLar Particle Acceleration in Coronal Shocks (SOLPACS) model, which is a proton acceleration simulation in shocks with self-consistent nonlinear wave–particle interactions. We compared a suprathermal monoenergetic injection with a two-component injection, including the suprathermal monoenergetic component and a broad-spectrum energetic component corresponding to the observed background particle spectrum. Energetic particles in the beginning of the simulation could increase the local wave intensities sufficiently to increase the rate of acceleration for injected particles and even reshape the resulting particle energy spectra and spatial distributions. The resulting particle energy spectra, particle spatial distributions, and wave intensity spectra are compared to observations made by Solar Orbiter’s instrument suite of the 2021 October 30 energetic storm particle (ESP) event to evaluate the relevance of the seed particle population in the acceleration model. Results. The energetic component of the seed particle population shortens the needed acceleration time for particles and enhances the tail of the spectrum to a level that matches the observations. The highest compared energies (> 1 MeV) match only when an energetic component is included in the seed particle population. The wave intensities and spatial distributions, on the other hand, showed no significant differences with the monoenergetic and two-component injection. While the simulated and observed wave intensities match within five minutes before the shock passing, the simulated wave field is too intense farther out from the shock, probably due to a lack of wave damping and/or decay processes in the simulation, leading to particles being slightly overly trapped to regions closer to the shock.

The onset of parametric decay of lower hybrid waves during lower hybrid current drive experiments on Experimental Advanced Superconducting Tokamak

Abstract An ad hoc calculation is presented to interpret the growth of sideband waves during lower hybrid current drive (LHCD) experiments on Experimental Advanced Superconducting Tokamak (EAST). We adopt the solution of the non-linear dispersion relation for parametric instabilities to describe the growth rate of ion cyclotron quasi-modes (ICQMs) in the peripheral plasma, and use the WKB solution of the propagation of electrostatic waves in two dimensions to model the variation of the electric field in the scrape-off-layer (SOL). We then calculate the growth rates and amplification factors of the sideband waves associated with ICQM in the parallel and perpendicular coupling limits. The onset and substantial growth of the first down-shifted sideband of lower hybrid waves (LHWs) are associated with elevation of the plasma density in the outer SOL where the growth rate of ICQM in the parallel coupling limit increases sharply after the density is elevated. The peak frequencies associated with the first harmonic of ICQM obtained from calculating the amplification factors in the parallel coupling limit ( A para ) agree very well with the observed frequencies of the first down-shifted sideband of 2.45 GHz LHWs in EAST pulse 43 772 and 86 521. The consistency between the calculation and the observation indicates that the sideband waves are associated with parametric decay instability of ICQM excited in the outer SOL through parallel coupling. The amplitude of A para obtained from a single pass of LHWs through the SOL of EAST is, however, one order of magnitude smaller than unity, meaning that it remains elusive whether the substantial growth of sideband waves mainly occurs in front of the antenna or requires multiple passes of LHWs across the SOL region.

Evolution of water wave packets by wind in shallow water

We use the Korteweg–de Vries (KdV) equation, supplemented with several forcing/friction terms, to describe the evolution of wind-driven water wave packets in shallow water. The forcing/friction terms describe wind-wave growth due to critical level instability in the air, wave decay due to laminar friction in the water at the air–water interface, wave stress in the air near the interface induced by a turbulent wind and wave decay due to a turbulent bottom boundary layer. The outcome is a modified KdV–Burgers equation that can be a stable or unstable model depending on the forcing/friction parameters. To analyse the evolution of water wave packets, we adapt the Whitham modulation theory for a slowly varying periodic wave train with an emphasis on the solitary wave train limit. The main outcome is the predicted growth and decay rates due to the forcing/friction terms. Numerical simulations using a Fourier spectral method are performed to validate the theory for various cases of initial wave amplitudes and growth and/or decay parameter ranges. The results from the modulation theory agree well with these simulations. In most cases we examined, many solitary waves are generated, suggesting the formation of a soliton gas.

Exploiting Axisymmetry to Optimize CFD Simulations—Heave Motion and Wave Radiation of a Spherical Buoy

Simulating the free decay motion and wave radiation from a heaving semi-submerged sphere poses significant computational challenges due to its three-dimensional complexity. By leveraging axisymmetry, we reduce the problem to a two-dimensional simulation, significantly decreasing computational demands while maintaining accuracy. In this paper, we exploit axisymmetry to perform a large ensemble of Computational Fluid Dynamics (CFDs) simulations, aiming to evaluate and maximize both accuracy and efficiency, using the Reynolds Averaged Navier–Stokes (RANS) solver interFOAM, in the opensource finite volume CFD software OpenFOAM. Validated against highly accurate experimental data, extensive parametric studies are conducted, previously limited by computational constraints, which facilitate the refinement of simulation setups. More than 50 iterations of the same heaving sphere simulation are performed, informing efficient trade-offs between computational cost and accuracy across various simulation parameters and mesh configurations. Ultimately, by employing axisymmetry, this research contributes to the development of more accurate and efficient numerical modeling in ocean engineering.

Experimental Study on Submerged Nozzle Damping Characteristics of Solid Rocket Motor

Acoustic instabilities in solid rocket motors (SRMs) can lead to severe performance deterioration and structural damage. Nozzle damping accounts for the main acoustic dissipation source, and it is highly dependent on geometric parameters and operating conditions. This study experimentally investigated the acoustic damping characteristics of submerged nozzles in SRMs, focusing on the effects of submerged cavity dimensions, nozzle convergent angle, throat-to-port area ratio, and mean pressure variations on the longitudinal instability. The steady-state wave decay method was used to quantify the acoustic damping, and a designed rotary valve system was employed to introduce periodic pressure oscillations in the high-pressure combustion chamber. The results revealed that a larger submerged cavity would reduce the nozzle damping efficiency, with the elimination of the submerged cavity enhancing the nozzle decay coefficient magnitude by 41.9%. Furthermore, increasing the nozzle convergent angle was found to amplify acoustic wave reflection, thereby diminishing damping performance. A linear inverse relationship was observed between the throat-to-port area ratio and the decay coefficient, with a 125% increase in the ratio resulting in a 24.3% reduction in the decay coefficient. Interestingly, despite the formation of complex vortices in the submerged cavity, the mean pressure variation presented negligible effects on acoustic damping characteristics, and its damping performance is similar to a simple nozzle without a cavity. These findings provide valuable experimental data for predicting the stability of a solid rocket motor with a submerged nozzle and offer insights into the optimization of submerged nozzle designs for higher acoustic damping in SRMs.

Spectra and decay properties of higher lying BC meson states

In this work, the spectra and decay properties of [Formula: see text] mesons [Formula: see text]) have been investigated using a nonrelativistic potential model incorporating corrections from LQCD. The nonrelativistic Schrödinger wave equation is solved numerically using the Matrix Numerov Method. Using the obtained masses and wave functions, decay widths, lifetime, branching ratios and radiative decay widths are computed for the [Formula: see text] system. Influence of the bound state effect on decay width of [Formula: see text] mesons is also analyzed. We compare the obtained results with the experimental data and with other theoretical models.

Stress Wave Propagation and Decay Based on Micro-Scale Modelling in the Topology of Polymer Composite with Circular Particles.

This article deals with stress wave decay performance, analysing the stress wave propagation generated by an impulsive unit load in a 2D representative unit cell (RUC) of a polymer composite with circular particles representing spherical particles, elliptical particles, and short fibres. The micro-scale numerical simulation uses explicit finite element analysis (FEA). The micro-response to an impulsive unit load creates a stress wave amplitude interacting with the material structure and tends to weaken and absorb energy. The stress wave damping is determined by the decaying amplitudes of Mises stress at the front of the stress wave. The stress wave damping is evaluated for different ratios of tensile modules and material densities of matrix and reinforcing material and other factors, such as percentage and particle size, applied to nine topologies of RUCs, and even the presence of an interfacial region is analysed. Moreover, the article visualises the phases of stress wave decay in various particle distributions, i.e., various topologies. Analysing the different topologies of the same particle volume (area) percentage, the study proved that the composite topology and resulting wave-particle and wave-wave interactions are other sources of material damping. The presence of even a small percentage, 3.5 area%, of reinforcing circular particles in the matrix brings a significant increase in stress wave damping up to about 40-43% (depending on the topology) compared to a homogeneous matrix with stress wave damping of 12.5% under the same conditions. Moreover, the topology with the same volume (area) percentage can increase particle stress wave damping by 15.3%.

Rayleigh wave in nonlocal piezo-thermo-electric semiconductor medium with fractional MGT model

This paper addresses a critical gap in Rayleigh wave propagation studies within piezoelectric semiconductors. Existing research often overlooks the combined effects of piezoelectricity, semiconductivity, and thermal behavior. This work presents analytical solutions for Rayleigh waves in a novel nonlocal thermo-piezo-photo-electric semiconductor half-space, employing the fractional Moore-Gibson-Thompson model. The wave-mode method and Durand-Kerner technique are employed to extract relevant solutions from the characteristic equation, ensuring surface wave decay. Analysis is conducted for waves propagating in a stress-free, photo-excited, and isothermal boundary condition. Numerical simulations unveil phase velocity, attenuation coefficient, and particle motion, leading to a deeper understanding of wave behavior. The influence of nonlocal and fractional order parameters is meticulously investigated. These findings reveal unique phenomena that significantly advance the comprehension of Rayleigh waves in these intricate materials.

Verification and validation of a coupled CFD–FEM approach with overset structured grid through free decay and regular wave tests

This paper presents a comprehensive verification and validation study applied to the hydrodynamic analysis of a semi-submersible Floating Offshore Wind Turbine (FOWT) platform. The numerical simulation is conducted using a coupled Computational Fluid Dynamics-Finite Element Method (CFD–FEM) approach. The CFD program incorporates an overset grid interpolation method, facilitating a more systematic grid refinement in the estimation of discretization uncertainties. A mooring analysis program, based on the FEM scheme, is integrated with the CFD program to simulate the dynamic responses of mooring system. The necessity of the nonlinear mooring model is demonstrated by comparing solutions with a comparative test using a linear mooring model. The verification study, based on a least-squares-based extrapolation method, quantifies the spatial and temporal discretization errors of the numerical model. The numerical solutions based on the baseline model are further validated against the model test measurements. A pitch free decay model test and a regular wave model test conducted within the OC5 project are utilized for the verification and validation study. Results from both tests demonstrate the reliability and accuracy of the coupled method.

Super-resolution by converting evanescent waves in microsphere to propagating waves and light transmitted from its surface to nano-jet

The electro-magnetic (EM) waves transmitted through a thin object with fine structures is observed, by microsphere located above the thin object. The EM radiation transmitted through the object produces both evanescent waves, which include information on the fine structures of the object (smaller than a wavelength), and propagating waves which include the large image of the object (with dimensions larger than a wavelength). The super-resolutions are calculated by using Helmholtz equation. According to this equation, evanescent waves have an imaginary component of the wavevector in the z direction, leading the components of the wavevector, in the transversal directions, to becomes very large, so that the fine structures of the object can be observed. Due to the decay of the evanescent waves, only a small region near the contact point, between the thin object and the microsphere is effective for producing the super resolution effects. The image with super-resolution can be increased by a movement of the microsphere over the object, or by using arrays of microspheres. Both propagating and evanescent waves arrive at the inner surface of the microsphere. A coupling between the transmitted EM waves and resonances produced in the dielectric sphere, possibly obtained by Mie method, leads to product of the EM distribution function with the transfer function. While this transfer function might be calculated by Mie method it is possible also to use it as an experimental function. By Fourier transform of the above product we get convolution between the EM spatial modes and those of the transfer function arriving at the nano-jet, which leads the evanescent waves to become propagating waves, with effective very small wavelengths, and thus increase the resolution.

Laser pulse-length dependent ablation and shock generation in silicon at 5×1014 W/ cm2 intensities

The effect of laser pulse duration on energy coupling into a planar silicon target is investigated in experiments at the OMEGA-EP facility by varying the laser pulse length τ—spanning 3 orders of magnitude from 100 ps to 10 ns—while maintaining a constant peak laser intensity, I0=5×1014 W/cm2. In theoretical models, the ablation pressure primarily scales for a given material with laser intensity and wavelength, which are all fixed variables here, allowing us to explore the specific role of laser pulse duration. Two-dimensional radiation-hydrodynamics simulations benchmarked with optical probing of the expanding plasma show that the pulse duration is critical for the ablation pressure to reach a steady state. Moreover, the pulse duration impacts shock decay and multiple wave effects, which strongly dictate the evolving shock profile that propagates within the laser-shocked target as ultimately measured by rear-surface diagnostics. The shock velocities inferred from the theoretical model, after considering shock decay, impedance matching, and shock Hugoniot, are found to be in good agreement with velocimetry measurements. However, discrepancies are observed with simulations for the shorter (0.1 ns) and longer (10 ns) pulse durations, which are respectively attributed to unaccounted contributions of kinetic absorption mechanisms and instabilities in simulations. Published by the American Physical Society 2024

Pinpointing the role of wave period in vegetation induced wave attenuation

Nature-based coastal protection that integrates vegetated wetlands for wave attenuation and erosion mitigation shows great potential. However, there is a lack of consensus on whether longer wave periods contribute to an increase or a reduction in the attenuation of waves in vegetated wetlands, which is primarily due to the disregard of vegetation submersion states. In the current study, we modified a classic model to pinpoint the conditional role of the period. Wave attenuation by vegetation is quantified as the product of two terms: wave decay rate and time of wave group travel through a unit length. By tracing the dynamics of these two terms, the model is in good agreement with the measurements and can well explain why wave attenuation increased with longer period (from 2 to 10 s) in submerged canopies (up to 10 times) but decreased in emergent canopies (by 75%). A maximum response period (2–10 s) was found, beyond which period has no effect on wave attenuation. Furthermore, we found that in field conditions, the variation in wave period can lead to a sharp reduction in wave dissipation. which is critical for coastal safety. For instance, a 62% decrease in wave period at Galveston Island corresponded to a 40% drop in wave dissipation. This work provides a comprehensive understanding on the role of wave period in wave dissipation by wetland vegetation, which would assist in safely implementing wetlands for coastal defence.

On the decay of viscous surface waves in 3D

We consider the incompressible viscous surface wave problem in the setting that the fluid domain is a horizontal infinite layer in 3D. The fluid dynamics is governed by the gravity-driven incompressible Navier–Stokes equations, and the effect of surface tension is ignored on the upper free surface. We prove the optimal time-decay rate of the low-order energy of the solution with minimal derivative count 3, which implies that the Lipschitz norm of the velocity decays at the rate (1+t)−1. This together with a time-weighted estimate for the highest order spatial derivatives of the free surface function leads to the boundedness of the high-order energy, which improves the result of Wang [9].

Tsunami Squares: Leapfrog scheme implementation and benchmark study on wave–shore interaction of solitary waves

Impulse waves are generated by rapid subaerial mass movements including landslides, avalanches and glacier break-offs, which pose a potential risk to public facilities and residents along the shore of natural lakes or engineered reservoirs. Therefore, the prediction and assessment of impulse waves are of considerable importance to practical engineering. Tsunami Squares, as a meshless numerical method based on a hybrid Eulerian–Lagrangian algorithm, have focused on the simulation of landslide-generated impulse waves. An updated numerical scheme referred to as Tsunami Squares Leapfrog, was developed which contains a new smooth function able to achieve space and time convergence tests as well as the Leapfrog time integration method enabling second-order accuracy. The updated scheme shows improved performance due to a lower wave decay rate per unit propagation distance compared to the original implementation of Tsunami Squares. A systematic benchmark testing of the updated scheme was conducted by simulating the run-up, reflection and overland flow of solitary waves along a slope for various initial wave amplitudes, water depths and slope angles. For run-up, the updated scheme shows good performance when the initial relative wave amplitude is smaller than 0.4. Otherwise, the model tends to underestimate the run-up height for mild slopes, while an overestimation is observed for steeper slopes. With respect to overland flow, the prediction error of the maximum flow height can be limited to ± 50% within a 90% confidence interval. However, the prediction of the front propagation velocity can only be controlled to ± 100% within a 90% confidence interval. Furthermore, a sensitivity analysis of the dynamic friction coefficient of water was performed and a suggested range from 0.01 to 0.1 was given for reference.

Coupling a nonlinear finite element mooring model with an overset CFD solver for dynamic analysis of floating structures in waves

An accurate prediction of motion responses of a moored floating structure requires high-fidelity coupled analysis between the structure and its mooring system in waves, which involves both mooring line dynamics and fluid dynamics. In this paper, we develop a nonlinear finite element dynamic mooring analysis module that allows large axial stretching of mooring lines under the open source CFD framework OpenFOAM, and couple it with an Overset CFD solver to establish a fully coupled finite element mooring-CFD analysis model for floating structures. The coupled model is advantageous over existing models in that it is able to deal with large axial mooring stretching and complex mesh motions induced by significant structure responses under severe operating conditions. The developed dynamic mooring analysis method is firstly validated against publicly available data. In order to validate the coupled model, a series of experimental tests were carried out for a semi-submersible platform moored by eight catenary lines under different operating conditions, including free decay, regular and irregular wave tests. The dynamic responses of the floating structure and mooring tension are analyzed and compared with experimental data. Results show that numerically predicted structure responses and mooring tension are generally in good agreement with experimental measurements. Meanwhile, the strongly nonlinear large-amplitude resonant motions generated by the interaction of irregular waves with the moored floating structure are also investigated. Comparisons reveal that the coupled model can accurately predict the resonant spectral peaks of the structure responses, indicating that the it is capable of simulating large-amplitude motions of moored floating structures. The coupled model developed in this paper can be further applied to study the survivability of moored floating structures under harsh sea conditions.

A Case Study of the Integration of Ground-Based and Drone-Based Ground-Penetrating Radar (GPR) for an Archaeological Survey in Hulata (Israel): Advancements, Challenges, and Applications

This study delves into the fusion of ground-based and drone-based ground-penetrating radar (GPR) technologies in archaeological exploration. Set against the backdrop of the Hulata solar panel construction site in Israel, the research confronts daunting obstacles such as clayey soil, accurate detection of small objects, and the imperative of timely reporting crucial for construction management. The drone-based GPR, a testament to technological innovation, showcases remarkable adaptability to challenging terrains, dispelling doubts about electromagnetic wave decay in clayey soil. Methodologically, the study employs detailed orthophoto mapping and grid-type surveys. The correlation of the results significantly bolsters the reliability of archaeological discoveries, uncovering scattered artifacts buried approximately 1–1.5 m below the surface. Meticulous excavations validate the geophysical surveys, affirming the presence of structures constructed from boulders. The application at the Hulata site validates the adaptability of drone-based GPR in challenging terrains. It provides a swift, cost-effective, and minimally invasive alternative to traditional excavation techniques, thereby transforming the field of archaeology.

Size-dependent effect on the interaction of surface waves in micropolar thermoelastic medium with dual pore connectivity

This research tackles a critical knowledge gap in Rayleigh surface wave propagation. It offers a comprehensive analysis that surpasses previous limitations. A size-dependent micropolar medium with unique void distributions and thermal effects is considered in this work. The constitutive relations and equations of motion for a nonlocal micropolar thermoelastic medium with double voids (MTMWDV) have been established by using Eringen’s nonlocal elasticity theory. Employing the three-phase-lag thermoelasticity theory (TPLTE), the study utilizes a wave-mode method to derive analytical solutions for Rayleigh waves in a nonlocal MTMWDV. To gain a comprehensive understanding of wave behavior, we solve the characteristic equation and analyze its roots, applying a filter based on the surface wave decay condition. A medium with stress-free and isothermal boundaries is explored through computational simulations to determine the attenuation coefficient and phase velocity. Furthermore, particle motion analysis is conducted to complement the analytical and computational approaches. Moreover, the influence of the nonlocal parameter and various thermoelastic models on these wave phenomena is investigated. The validity of the current mathematical model is confirmed through the derivation of particular scenarios.

Parametric resonance of Alfvén waves driven by ionization-recombination waves in the weakly ionized solar atmosphere.

Parametric coupling of waves is one of the most efficient mechanisms of energy transfer that can lead to the growth or decay of waves. This transfer occurs at frequencies close to their natural frequencies. In partially ionized solar plasma, there are a multitude of waves that can undergo this process. Here, we study the parametric coupling of Alfvén waves propagating in a partially ionized solar plasma with ionization-recombination waves identified by our study to appear in a plasma in ionization non-equilibrium. Depending on the parameters that describe the plasma (density, temperature), coupling can lead to a parametric resonance. Our study determines the occurrence conditions of parametric resonance, by finding the boundaries between stable and unstable regions in the parameter space. Our results show that collisions and non-equilibrium recombination can both contribute to the onset of unstable behaviour of parametrically resonant Alfvén waves. This article is part of the theme issue 'Partially ionized plasma of the solar atmosphere: recent advances and future pathways'.