Phase Velocity Of Propagation Research Articles

Plane waves in temperature dependent hygrothermoelastic medium under the influence of gravity—Analytical and numerical approach

AbstractThe present research article deals with the study of surface wave propagation in a temperature rate‐dependent hygrothermoelastic medium under the influence of gravity. The coupled wave equations in terms of displacement, temperature, and moisture concentration are solved analytically. The values of propagation phase velocity and attenuation quality factor for different waves have been obtained and depicted graphically against frequency. The effect of the gravity field and the dependence of temperature on the quantities are presented graphically. The coupled and independent wave equations obtained, are solved analytically and numerically to obtain the values of propagation phase velocities. The graphical results of propagation phase velocity and attenuation quality factor are compared for analytical and numerical results.

Acoustical characteristics of solid elastic mediums with oriented microfructures

Model for interaction of plane elastic longitudinal waves with contains oriented microfractures with specific boundary conditions for “linear slip@ approximation is developed. The form of dispersion equation is defined in approximation of Bloch and Floque waves theory. Results of its solution which define character of functions for propagation phase velocity and attenuation coefficient of effective longitudinal wave in dependence on crack faces microfracture parameters and other model parameters.

The Role of Ambient Turbulence in Canopy Wave Generation by Kelvin–Helmholtz Instability

We test the hypothesis that internal waves observed in flow over forest canopies are generated by Kelvin–Helmholtz instability. The waves were observed at night, under stably stratified and weak wind conditions, with a horizontally scanning aerosol lidar and an instrumented tower. The lidar images are used to determine the salient wavelength and phase propagation velocity of each episode. Time series data measured at the tower are then used to form vertical profiles of background velocity and buoyancy just before each observed wave event. The profiles are input to the Taylor–Goldstein equation to predict the phase velocity, wavelength and period of the fastest-growing linear instability, and the results compared with the lidar observations. The observed wavelengths tend to be longer than predicted by the Taylor–Goldstein theory, typically by a factor of two. That discrepancy is removed when the theory is extended to account for the effects of ambient, small-scale turbulence.

Multispacecraft wave analysis of current sheet flapping motions in Earth’s magnetotail

In our work, for the first time, we conducted a comprehensive multispacecraft wave study of flapping current sheet oscillations in Earth’s magnetotail. Measurements taken from the Magnetospheric Multiscale (MMS) mission were analyzed for two flapping events with different morphologies of oscillation behavior: stationary-like and kink-like type. A comparison of the results calculated by the methods of phase difference, wave surveyor, and Multipoint Signal Resonator technique was carried out. For the first time, using observations, it was found that the energy distribution of wavy magnetic field contains complex multi-branch dispersion dependencies on ky and kz. The phase velocities of propagation of flapping oscillations were estimated. The used methods complement each other, and their differences made it possible to assess the presence of non-linear wave packets during kink flapping and the azimuthal asymmetry of the current sheet profile.

Study of geological processes of absorption of pressure waves from injected fluids in the rock structure

The paper presents a detailed study of the propagation of oscillations in an infinite absorbing medium in order to discuss the behavior of a material under various conditions during pulsed injection of fluids into an injection well. The dependence of deformation and stress was solved mathematically on the basis of the modified Hooke’s law, which includes the rate of change in deformation. As a result, graphical dependences of the phase velocity of propagation of oscillations and the absorption coefficient on the oscillation frequency were obtained for the most common types of rocks. Analysis of the obtained results showed that the absorption coefficient attains its maximum values in the region of resonance frequencies, and further increase in the oscillation frequency leads to a slight decrease in the absorption coefficient. In our opinion, the most optimal frequency range for the propagation of oscillations in the rock structure varies from 100 to 800 Hz with regard to the natural frequencies of the rocks studied.

Anomalous azimuthal variations with 360° periodicity of Rayleigh phase velocities observed in Scandinavia

SUMMARY We use the recently deployed ScanArray network of broad-band stations covering most of Norway and Sweden as well as parts of Finland to analyse the propagation of Rayleigh waves in Scandinavia. Applying an array beamforming technique to teleseismic records from ScanArray and permanent stations in the study region, in total 159 stations with a typical station distance of about 70 km, we obtain phase velocities for three subregions, which collectively cover most of Scandinavia (excluding southern Norway). The average phase dispersion curves are similar for all three subregions. They resemble the dispersion previously observed for the South Baltic craton and are about 1 per cent slower than the North Baltic shield phase velocities for periods between 40 and 80 s. However, a remarkable sin(1θ) phase velocity variation with azimuth is observed for periods >35 s with a 5 per cent deviation between the maximum and minimum velocities, more than the overall lateral variation in average velocity. Such a variation, which is incompatible with seismic anisotropy, occurs in northern Scandinavia and southern Norway/Sweden but not in the central study area. The maximum and minimum velocities were measured for backazimuths of 120° and 300°, respectively. These directions are perpendicular to a step in the lithosphere–asthenosphere boundary (LAB) inferred by previous studies in southern Norway/Sweden, suggesting a relation to large lithospheric heterogeneity. In order to test this hypothesis, we carried out 2-D full-waveform modeling of Rayleigh wave propagation in synthetic models which incorporate a steep gradient in the LAB in combination with a pronounced reduction in the shear velocity below the LAB. This setup reproduces the observations qualitatively, and results in higher phase velocities for propagation in the direction of shallowing LAB, and lower ones for propagation in the direction of deepening LAB, probably due to the interference of forward scattered and reflected surface wave energy with the fundamental mode. Therefore, the reduction in lithospheric thickness towards southern Norway in the south, and towards the Atlantic ocean in the north provide a plausible explanation for the observed azimuthal variations.

Complete phenomenon of reflection at the plane boundary of a dissipative anisotropic elastic medium

SUMMARYA complex slowness vector governs the 3-D propagation of harmonic plane waves in a dissipative elastic medium with general anisotropy. In any sagittal plane, this dual vector is specified with phase direction, propagation velocity and coefficients for attenuation. A generalized reflection phenomenon is illustrated for incidence of inhomogeneous waves at the stress free boundary of the medium. Each reflected wave at the boundary is characterized by its propagation direction, propagation velocity, inhomogeneity, amplitude ratio, phase shift and energy flux. These propagation characteristics are exhibited graphically for a numerical example of anisotropic viscoelastic medium.

Formation of Multilayered Sporadic E under an Influence of Atmospheric Gravity Waves (AGWs)

The formation of multilayered sporadic E by atmospheric gravity waves (AGWs), propagating in the mid-latitude lower thermosphere, is shown theoretically and numerically. AGWs with a vertical wavelength smaller than the width of the lower thermosphere lead to the appearance of vertical drift velocity nodes (regions where the ions’ vertical drift velocity, caused by these waves, is zero) of heavy metallic ions (Fe+). The distance between the nearest nodes is close to the AGWs’ vertical wavelength. When the divergence of the ion vertical drift velocity at its nodes has a minimal negative value, then these charged particles can accumulate into Es-type thin layers and the formation of multilayered sporadic E is possible. We showed the importance of the ions’ ambipolar diffusion in the formation of Es layers and control of their densities. Oblique downward or upward propagation of AGWs causes downward or upward motion of the ion vertical drift velocity nodes by the vertical propagation phase velocity of these waves. In this case, the formed Es layers also descend or move upward with the same phase velocity. The condition, when the horizontal component of AGWs’ intrinsic phase velocity (phase velocity relative to the wind) and background wind velocity have same magnitudes but opposite directions, is favorable for the formation of the multilayered sporadic E at fixed heights of the sublayers. When the AGWs are absent, then horizontal homogeneous wind causes the formation of sporadic E but with a single peak. In the framework of the suggested theory, it is shown that, in the lower thermosphere, the wind direction, magnitude, and shear determine the development of the processes of ion/electron convergence into the Es-type layer, as well as their density divergence. Consideration of arbitrary height profiles of the meridional and zonal components of the horizontal wind velocity, in case of AGW propagation, should be important for the investigation of the distribution and behavior of heavy metallic ions on regional and global scales.

Migrating Seismicity in the Lithosphere of the Baikal Rift Zone: Spatiotemporal and Energy Distribution of Earthquake Chains

Abstract ––Quasi-linear sequences of the epicenters of strong earthquakes, identified in many seismically active regions, are phenomenologically viewed as “migrations” of earthquake sources. Following this analogy, an earthquake chain is understood in this paper as a set of seismic events of different energies, leading to a quasi-linear one-way change in the position (“migration”) of the successive epicenters of shocks on the surface of the lithosphere zone under study. Based on this statement, a formalized method for an azimuthal analysis of seismicity is developed, which allows one to identify and isolate earthquake chains from arrays of seismological data presented in the standard format of a catalog of earthquakes. As this method is tested on a catalog of earthquakes and a catalog of simulation events, all model chains of events and a large number of earthquake chains and simulation events are identified. It is indicated by isolating chains in a random field of simulation events that some of these earthquake chains can be formed by a random spatiotemporal combination of shocks. Migrating seismicity in the lithosphere of the Baikal rift zone (BRZ) is studied by applying the method of identification and isolation of earthquake chains to materials from the “Catalog of Earthquakes of the Baikal region”. According to data on 52,700 earthquakes with a representative energy class KP ≥ 8, occurring in the Baikal region from 1964 to 2013, there are 2143 earthquake chains identified and isolated within an angular sector of azimuthal analysis q = 10° (±5° from azimuth α to the epicenter). As the angular sector of azimuthal analysis increases to q = 20° (±10°), there is an approximately twofold increase in the number of chains (M = 4245). As shown by the analysis and comparison of spatiotemporal distribution of earthquakes and earthquake chains, the spatiotemporal and energy distribution of chains of seismic events is formed by earthquake distribution in the BRZ. Beyond this zone, the chains are small in number. The established relationship between the distributions of earthquakes and earthquake chains in space, in time, and by energy indicates that in the epicentral field of seismicity of the BRZ, both “seismicity migration” chains and randomly formed chains (“pseudomigration” chains) are identified. The migrating seismicity of the BRZ is studied according to the seismicity statistics by using the criteria developed within the framework of the simulation base model of migrating seismicity to the results obtained. An index of seismicity migration activity (ISMA) that reflects a seismicity migration/pseudomigration ratio at the set level of significance is used to obtain distribution maps over the territory and graphs of changes over the years for this index. The maps show that small areas ISMA > 1 are seen in close proximity to rifting attractor structures (RASs), while seismicity migration in the rest of the BRZ is not statistically obvious. The graphs show that periods ISMA > 1 at three levels of significance are observed three to four years after the activation of RASs, which makes it possible to estimate the phase propagation velocity of a slow deformation perturbation of about 250–300 km/year. It is indicated by the results obtained that the migrating seismicity of the BRZ is directly related to the location and activations of RASs and that the RASs are the sources of local deformation perturbations in the BRZ lithosphere, which, among other things, manifest themselves in the implementation of seismicity migration chains.

Application of computer vision and neural network analysis to study the structure and dynamics of turbulent jets

In this paper we solved the problem of detecting and detailed analysis of the characteristics of coherent structures in non-swirling and swirling turbulent jets from the 3D PIV experiment and DNS modelling database. To solve the problem intellectual approaches of computer vision based on deep neural networks were applied. It is shown that with the use of a generative competitive neural network, it is possible to reconstruct the structure and dynamics of a turbulent flow with an increased spatial resolution, which is important for analysis and interpretation. The approach is based on a modification of the loss function, which minimizes the residual part of the hydrodynamic equations (the continuity equations and the Poisson equation) for the reconstructed data. It is shown that generative models are more effective in the reconstruction of high moments of turbulent flow than conventional methods POD and DMD. Using a fully convolutional neural network, an automatic segmentation of the turbulent jet flow region and the external environment based on instantaneous velocity and pressure fields was carried out. For a swirling jet, the area of reversed flow is identified. It is shown that the complex of the developed machine learning algorithms successfully copes with the localization of coherent structures, the detection of their trajectory, characteristic size and phase propagation velocity. The obtained new fundamental information is important for a deeper understanding of the role of vortex structures in mixing processes in a jet flow. The developed complex of algorithms for the identification and analysis of characteristics of coherent structures can be applied to a database of measurements and numerical simulation of a wide class of hydrodynamic flows.

Initial transport and turbulence analysis and gyrokinetic simulation validation in NSTX-U L-mode plasmas

Transport analysis, ion-scale turbulence measurements, and initial linear and nonlinear gyrokinetic simulations are reported for a transport validation study based on low aspect ratio NSTX-U L-mode discharges. The relatively long, stationary L-modes enabled by the upgraded centerstack provide a more ideal target for transport validation studies that were not available during NSTX operation. Transport analysis shows that anomalous electron transport dominates energy loss while ion thermal transport is well described by neoclassical theory. Linear gyrokinetic GYRO analysis predicts that ion temperature gradient (ITG) modes are unstable around normalized radii ρ = 0.6–0.8, although E × B shearing rates are larger than the linear growth rates over much of that region. Deeper in the core (ρ = 0.4–0.6), electromagnetic microtearing modes (MTM) are unstable as a consequence of the relatively high beta and collisionality in these particular discharges. Consistent with the linear analysis, local, nonlinear ion-scale GYRO simulations predict strong ITG transport at ρ = 0.76, whereas electromagnetic MTM transport is important at ρ = 0.47. The prediction of ion-scale turbulence is consistent with 2D beam emission spectroscopy (BES) that measures the presence of broadband ion-scale fluctuations. Interestingly, the BES measurements also indicate the presence of bi-modal poloidal phase velocity propagation that could be indicative of two different turbulence types. However, in the region between (ρ = 0.56, 0.66), ion-scale simulations are strongly suppressed by the locally large E × B shear. Instead, electron temperature gradient (ETG) turbulence simulations predict substantial transport, illustrating electron-scale contributions can be important in low aspect ratio L-modes, similar to recent analysis at conventional aspect ratio. However, agreement within experimental uncertainties has not been demonstrated, which requires additional simulations to test parametric sensitivities. The potential need to include profile-variation effects (due to the relatively large value of ρ* = ρi/a at low aspect ratio), including electromagnetic and possibly multi-scale effects, is also discussed.

Experimental constraint on the radial mode number of the geodesic acoustic mode from multi-point Langmuir probe measurements in MAST Ohmic plasma

Reciprocating Mach probe data is used to estimate the radial wave number of oscillatory zonal flows in Ohmic MAST plasma. An intermittent ∼10 kHz mode, previously identified as a geodesic acoustic mode (GAM), is detected in the wavelet decomposition and windowed spectra of plasma potential fluctuations of the MAST tokamak edge plasma. Two-points phase differencing technique is then applied to probe pins with radial and poloidal separations giving an estimate of the radial wave number at the desired range of frequencies. The phase velocity of propagation and an estimate of the shearing rate of the GAM is obtained. We measure the radial mode number range kr ≈ 0.3–1.0 cm−1 and a radial propagation speed of up to ∼1 km s−1. The GAM shearing rate is an order of magnitude smaller than the growth rate of drift-like turbulence. These results are consistent with the estimates obtained previously from multi-fluid numerical simulations of GAM in MAST.

Studying internal gravity waves generated by atmospheric fronts over the Moscow region

Internal gravity wave (IGW) data obtained during the passage of atmospheric fronts over the Moscow region in June–July 2015 is analyzed. IGWs were recorded using a group of four microbarographs (developed at the Obukhov Institute of Atmospheric Physics, Russian Academy of Sciences) located at distances of 7 to 54 km between them. Regularities of variations in IGW parameters (spatial coherence, characteristic scales, propagation direction, horizontal propagation velocity, and amplitudes) before, during, and after the passage of an atmospheric front over the observation network, when the observation network finds itself inside the cyclone and outside the front, are studied. The results may be useful in studying the relationships between IGW effects in different physical fields at different atmospheric heights. It is shown that, within periods exceeding 30 min, IGWs are coherent between observation points horizontally spaced at distances of about 60 km (coherence coefficient is 0.6–0.9). It is also shown that there is coherence between wave fluctuations in atmospheric pressure and fluctuations in horizontal wind velocity within the height range 60–200 m. A joint analysis of both atmospheric pressure and horizontal wind fluctuations has revealed the presence of characteristic dominant periods, within which cross coherences between fluctuations in atmospheric pressure and wind velocity have local maxima. These periods are within approximate ranges of 20–29, 37–47, 62–72, and 100–110 min. The corresponding (to these dominant periods) phase propagation velocities of IGWs lie within an interval of 15–25 m/s, and the horizontal wavelengths vary from 52 to 99 km within periods of 35 to 110 min, respectively.

Multi-dimensional [formula omitted]-fractional diffusion–wave equation and some properties of its fundamental solution

In this paper, a multi-dimensional α-fractional diffusion–wave equation is introduced and the properties of its fundamental solution are studied. This equation can be deduced from the basic continuous time random walk equations and contains the Caputo time-fractional derivative of the order α/2 and the Riesz space-fractional derivative of the order α so that the ratio of the derivatives orders is equal to one half as in the case of the conventional diffusion equation. It turns out that the α-fractional diffusion–wave equation inherits some properties of both the conventional diffusion equation and of the wave equation. In particular, in the one- and two-dimensional cases, the fundamental solution to the α-fractional diffusion–wave equation can be interpreted as a probability density function and the entropy production rate of the stochastic process governed by this equation is exactly the same as the case of the conventional diffusion equation. On the other hand, in the three-dimensional case this equation describes a kind of anomalous wave propagation with a time-dependent propagation phase velocity.

Wave propagation analysis of a functionally graded magneto-electro-elastic nanobeam rest on Visco-Pasternak foundation

Wave propagation analysis of a nanobeam made of functionally graded magneto-electro-elastic materials with rectangular cross section rest on Visco-Pasternak foundation is studied in this paper. For modeling the axial, rotation and transverse deformations, Timoshenko beam model is used. Fundamental magneto-electro-elastic equations of the model are derived for a general functionally graded beam excited to electric and magnetic potentials. Surface elasticity is employed for more confident modeling the behavior of nanobeam. Using Hamilton principle and calculation of kinetic and strain energies, the equations of motion are derived. Considering the harmonic wave propagation of infinite domain yields characteristic equation of the system in terms of different parameters of model. The effects of different parameters such as non-homogeneous index, wave number and residual surface stress are investigated on the different phase velocities corresponding to modes of deformation. One can find that increasing the non-homogeneous index and wave number leads to decrease in wave propagation phase velocities.

A sharp interface method for coupling multiphase flow, heat transfer and multicomponent mass transfer with interphase diffusion

Mixing of partially miscible fluids plays an important role in many physical and chemical processes. The modeling complexities lie in the tight coupling of the multiphase flow, heat transfer and multicomponent mass transfer, as well as diffusions across the phase interface. We present a sharp interface method for modeling such process. The non-ideal equation of state is used to compute the fluid properties such as density, fugacity and enthalpy, and to predict phase equilibrium composition. The phase interface location is tracked using the phase propagation velocity. A third-order one-sided finite difference scheme using a variable grid size according to the interface location is utilized to discretize the partial derivatives immediately next to the interface, while a second-order central scheme is used for the bulk of fluids. An optimization method, the Nelder–Mead method, is applied to search for (1) the phase compositions on both sides of the interface, and (2) the phase propagation velocity based on the coupling of the multicomponent phase equilibrium and the species' balance across the interface. The temperature at the interface is determined by the energy balance. Numerical results are used to demonstrate the convergence of our method and show its capability to simulate the mixing of multicomponent partially miscible fluids.

Variable phase propagation velocity for long‐range lightning location system

AbstractThe electromagnetic wave propagation velocity at low radio frequencies is an important input parameter for lightning location systems that use time of arrival (TOA) method. This velocity is normally fixed at or near the speed of light. However, this study finds that the radio waves from two submarine communication transmitters at 20.9 kHz and 23.4 kHz exhibit phase propagation velocities that are ~0.51% slower and ~0.64% faster than the speed of light as a result of sky wave contributions and ground effects. Therefore, a novel technique with a variable phase propagation velocity is implemented for the first time in the TOA method and applied to electric field recordings with a long‐baseline lightning location system that consists of four radio receivers in western Europe. The lightning locations inferred from variable velocities improve the accuracy of locations inferred from a fixed velocity by ~0.89–1.06 km when compared to the lightning locations reported by the UK MetOffice. The normal distributions of the observed phase propagation velocities in small geographic areas are not centered at the speed of light. Consequently, representative velocities can be calculated for many small geographic areas to produce a velocity map over central France where numerous lightning discharges occurred. This map reflects the impact of sky waves and ground effects on the calculation of lightning locations as a result of the network configuration. It is concluded that the use of variable phase propagation velocities mitigates the influence of sky waves and ground effects in long‐range lightning location networks.

Asymmetry in the Farley‐Buneman dispersion relation caused by parallel electric fields

AbstractAn implicit assumption utilized in studies of E region plasma waves generated by the Farley‐Buneman instability (FBI) is that the FBI dispersion relation and its solutions for the growth rate and phase velocity are perfectly symmetric with respect to the reversal of the wave propagation component parallel to the magnetic field. In the present study, a recently derived general dispersion relation that describes fundamental plasma instabilities in the lower ionosphere including FBI is considered and it is demonstrated that the dispersion relation is symmetric only for background electric fields that are perfectly perpendicular to the magnetic field. It is shown that parallel electric fields result in significant differences between the growth rates and phase velocities for propagation of parallel components of opposite signs. These differences are evaluated using numerical solutions of the general dispersion relation and shown to exhibit an approximately linear relationship with the parallel electric field near the E region peak altitude of 110 km. An analytic expression for the differences is also derived from an approximate version of the dispersion relation, with comparisons between numerical and analytic results agreeing near 110 km. It is further demonstrated that parallel electric fields do not change the overall symmetry when the full 3‐D wave propagation vector is reversed, with no symmetry seen when either the perpendicular or parallel component is reversed. The present results indicate that moderate‐to‐strong parallel electric fields of 0.1–1.0 mV/m can result in experimentally measurable differences between the characteristics of plasma waves with parallel propagation components of opposite polarity.

Signal velocity in oscillator arrays

We investigate a system of coupled oscillators on the circle, which arises from a simple model for behavior of large numbers of autonomous vehicles where the acceleration of each vehicle depends on the relative positions and velocities between itself and a set of local neighbors. After describing necessary and sufficient conditions for asymptotic stability, we derive expressions for the phase velocity of propagation of disturbances in velocity through this system. We show that the high frequencies exhibit damping, which implies existence of well-defined signal velocities c + > 0 and c − < 0 such that low frequency disturbances travel through the flock as f +(x − c + t) in the direction of increasing agent numbers and f −(x − c − t) in the other.

Effects of piezoelectricity on bulk waves in monoclinic poro-elastic materials

Piezoelectric materials are materials which produce electric field when stress is applied and get strained when electric field is applied. Piezoelectric materials are acting as very important functional components in sonar projectors, fluid monitors, pulse generators and surface acoustic wave devices. Wave propagation in porous piezoelectric material having crystal symmetry 2 is studied analytically. The Christoffel equation is derived. The phase velocities of propagation of all these waves are described in terms of complex wave velocities. The effects of phase direction, porosity, wave frequency and piezoelectric interaction on the phase velocities are studied numerically for a particular model.