Showing papers on "Longitudinal wave published in 2005"

The degeneration of internal waves in lakes with sloping topography

Abstract: In a laboratory study, we quantified the temporal energy flux associated with the degeneration of basin-scale internal waves in closed basins. The system is two-layer stratified and subjected to a single forcing event creating available potential energy at time zero. A downscale energy transfer was observed from the wind-forced basin-scale motions to the turbulent motions, where energy was lost due to high-frequency internal wave breaking along sloping topography. Under moderate forcing conditions, steepening of nonlinear basin-scale wave components was found to produce a high-frequency solitary wave packet that contained as much as 20% of the available potential energy introduced by the initial condition. The characteristic lengthscale of a particular solitary wave was less than the characteristic slope length, leading to wave breaking along the sloping boundary. The ratio of the steepening timescale required for the evolution of the solitary waves to the travel time until the waves shoaled controlled their development and degeneration within the domain. The energy loss along the slope, the mixing efficiency, and the breaker type were modeled using appropriate forms of an internal Iribarren number, defined as the ratio of the boundary slope to the wave slope (amplitude/wavelength). This parameter allows generalization to the oceanographic context. Analysis of field data shows the portion of the internal wave spectrum for lakes, between motions at the basin and buoyancy scales, to be composed of progressive waves: both weakly nonlinear waves (sinusoidal profile with frequencies near 10 24 Hz) and strongly nonlinear waves (hyperbolic‐secant-squared profile with frequencies near 10 23 Hz). The results suggest that a periodically forced system may sustain a quasi-steady flux of 20% of the potential energy introduced by the surface wind stress to the benthic boundary layer at the depth of the pycnocline.

On radar imaging of current features: 1. Model and comparison with observations

Abstract: [1] A new radar imaging model of ocean current features is proposed. The simulated normalized radar cross section (NRCS) takes into account scattering from ‘‘regular’’ surfaces (by means of resonant Bragg scattering and specular reflections) and scattering from breaking waves. The description of background wind waves and their transformation in nonuniform medium is based on solution of the wave action conservation equation. Wave breaking plays a key role in the radar imaging model. Breaking waves scatter radio waves (thus directly contributing to the NRCS), provide energy dissipation in wind waves (thus defining the wave spectrum of intermediate scale waves), and generate short surface waves (thus affecting Bragg scattering). Surface current, surfactants accumulated in the convergence zone, and varying wind field are considered as the main sources for the NRCS manifestations of current features. The latter source can result from transformation of atmospheric boundary layer over the sea surface temperature front. It is shown that modulation of wave breaking significantly influences both radar returns and short wind waves. In the range of short gravity waves related to Ku- X-, and C-bands, the modulation of Bragg waves through wave breaking is the governing mechanism. The model is tested against well-controlled experiments including JOWIP, SARSEX, and CoastWatch-95. A reasonably good agreement between model and observations is obtained.

Modulation instability of Stokes wave → freak wave

Abstract: Formation of waves of large amplitude (freak waves, killer waves) at the surface of the ocean is studied numerically. We have observed that freak waves have the same ratio of the wave height to the wave length as limiting Stokes waves. When a freak wave reaches this limiting state, it breaks. The physical mechanism of freak wave formation is discussed.

Compressional and shear wave properties of marine sediments: comparisons between theory and data.

Abstract: According to a recently developed theory of wave propagation in marine sediments, the dispersion relationships for the phase speed and attenuation of the compressional and the shear wave depend on only three macroscopic physical variables: porosity, grain size, and depth in the sediment. The dispersion relations also involve three (real) parameters, assigned fixed values, representing microscopic processes occurring at grain contacts. The dispersion relationships are compared with extensive data sets, taken from the literature, covering the four wave properties as functions of all three physical variables. With no adjustable parameters available, the theory matches accurately the trends of all the data sets. This agreement extends to the compressional and shear attenuations, in that the theory accurately traces out the lower bound to the widely distributed measured attenuations: the theory predicts the intrinsic attenuation, arising from the irreversible conversion of wave energy into heat, whereas the measurements return the effective attenuation, which includes the intrinsic attenuation plus additional sources of loss such as scattering from shell fragments and other inhomogeneities in the medium. Provided one wave or physical property is known, say the compressional speed or the porosity, all the remaining sediment properties may be reliably estimated from the theory.

Receptivity of a supersonic boundary layer over a flat plate. Part 3. Effects of different types of free-stream disturbances

Abstract: Supersonic boundary-layer receptivity to different types of free-stream disturbance is studied for a Mach 4.5 boundary-layer flow over a flat plate by using the approaches of both direct numerical simulation and linear stability theory. This paper is Part 3 of a three-part study of the receptivity of supersonic boundary layers to free-stream disturbances. The present paper investigates receptivity to four types of different free-stream disturbances, i.e. slow and fast acoustic waves, entropy waves, and vorticity waves. A high-order shock-fitting scheme is used in the numerical simulation in order to accurately account for the effects of interactions between free-stream disturbance waves and the oblique shock wave. Numerical results on the generation of fast acoustic waves by free-stream entropy waves or vorticity waves are compared with those of a linear theory. Good agreement is obtained in both wave angles and amplitudes immediately behind the bow shock. It is found that the second-mode receptivity to free-stream slow acoustic waves is several times stronger than that to free-stream fast acoustic waves. This is because free-stream slow acoustic waves can directly induce and interact with the first and second Mack modes, while free-stream fast acoustic waves cannot. Instead, the free-stream fast acoustic waves can only induce and interact with stable mode I waves, which in turn induce unstable Mack modes. In the cases of receptivity to free-stream entropy waves and vorticity waves, it is found that the oblique shock wave created by the displacement of the boundary layer plays an important role because boundary-layer disturbances are mainly induced by fast acoustic waves generated behind the shock by free-stream forcing waves. As a result, mechanisms of the receptivity to free-stream entropy and vorticity waves are very similar to those of the receptivity to free-stream fast acoustic waves.

Transverse waves in a post-flare supra-arcade

Abstract: Observations of propagating transverse waves in an open magnetic field structure with the Transition Region And Coronal Explorer (TRACE) are presented. Waves associated with dark tadpole-like sunward moving structures in the post-flare supra-arcade of NOAA active region 9906 on the 21st of April 2002 are analysed. They are seen as quasi-periodic transverse displacements of the dark tadpole tails, with periods in the range of 90–220 s. Their phase speeds and displacement amplitudes decrease as they propagate sunwards. At heights of 90 and 60 Mm above the post-flare loop footpoints the phase speeds are in the ranges 200–700 km s −1 and 90–200 km s −1 respectively. Furthermore, for consecutive tadpoles the phase speeds decrease and periods increase as a function of time. The waves are interpreted as propagating fast magnetoacoustic kink waves guided by a vertical, evolving, open structure.

Wave-induced fluid flow in random porous media: Attenuation and dispersion of elastic waves

Abstract: A detailed analysis of the relationship between elastic waves in inhomogeneous, porous media and the effect of wave-induced fluid flow is presented. Based on the results of the poroelastic first-order statistical smoothing approximation applied to Biot’s equations of poroelasticity, a model for elastic wave attenuation and dispersion due to wave-induced fluid flow in 3-D randomly inhomogeneous poroelastic media is developed. Attenuation and dispersion depend on linear combinations of the spatial correlations of the fluctuating poroelastic parameters. The observed frequency dependence is typical for a relaxation phenomenon. Further, the analytic properties of attenuation and dispersion are analyzed. It is shown that the low-frequency asymptote of the attenuation coefficient of a plane compressional wave is proportional to the square of frequency. At high frequencies the attenuation coefficient becomes proportional to the square root of frequency. A comparison with the 1-D theory shows that attenuation is of the same order but slightly larger in 3-D random media. Several modeling choices of the approach including the effect of cross correlations between fluid and solid phase properties are demonstrated. The potential application of the results to real porous materials is discussed.

Three-dimensional global hybrid simulation of dayside dynamics associated with the quasi-parallel bow shock

Abstract: [1] A three-dimensional global-scale hybrid simulation is carried out, for the first time, for dynamics of the dayside bow shock-magnetosphere system associated with the quasi-parallel bow shock A case with IMF along the Sun-Earth line is examined in detail First, the foreshock waves and the associated shock reformation process are investigated In particular, the generation and structure of diamagnetic cavities, with a decrease in the magnetic field and density, in the foreshock of the quasi-parallel shock are discussed Second, the interaction of the foreshock-originated pressure pulses with the dayside magnetosphere is simulated The diamagnetic cavities that are generated in the turbulent foreshock due to the ion beam plasma interaction are found to lead to strong surface perturbations at the magnetopause Third, the coupling between the pressure pulses and the magnetosphere is studied The compressional waves are found to mode convert to shear Alfven waves and kinetic Alfven waves through the Alfven resonance process in nonuniform plasmas The shear Alfven waves lead to field line resonance, which corresponds to the fundamental odd resonance wave number, and produce field-aligned currents in the dipole magnetospheric field

Theory of ``frozen waves'': modeling the shape of stationary wave fields

Abstract: In this work, starting by suitable superpositions of equal-frequency Bessel beams, we develop a theoretical and experimental methodology to obtain localized stationary wave fields (with high transverse localization) whose longitudinal intensity pattern can approximately assume any desired shape within a chosen interval 0⩽z⩽L of the propagation axis z. Their intensity envelope remains static, i.e., with velocity v=0, so we have named “frozen waves” (FWs) these new solutions to the wave equations (and, in particular, to the Maxwell equation). Inside the envelope of a FW, only the carrier wave propagates. The longitudinal shape, within the interval 0⩽z⩽L, can be chosen in such a way that no nonnegligible field exists outside the predetermined region (consisting, e.g., in one or more high-intensity peaks). Our solutions are notable also for the different and interesting applications they can have—especially in electromagnetism and acoustics—such as optical tweezers, atom guides, optical or acoustic bistouries, and various important medical apparatuses.

Travelling Waves and Periodic Oscillations in Fermi-Pasta-Ulam Lattices

Abstract: Infinite Lattice Systems Time Periodic Oscillations Travelling Waves: Waves with Prescribed Speed Travelling Waves: Further Results.

Plane waves in viscoelastic anisotropic media—I. Theory

Abstract: SUMMARY Properties of homogeneous and inhomogeneous plane waves propagating in an unbounded viscoelastic anisotropic medium in an arbitrarily specified direction N are studied analytically. The method used for their calculation is based on the so-called mixed specification of the slowness vector. It is quite universal and can be applied to homogeneous and inhomogeneous plane waves propagating in perfectly elastic or viscoelastic, isotropic or anisotropic media. The method leads to the solution of a complex-valued algebraic equation of the sixth degree. Standard methods can be used to solve the algebraic equation. Once the solution has been found, the phase velocities, exponential decays of amplitudes, attenuation angles, polarization vectors, etc., of P, S1 and S2 plane waves, propagating along and against N, can be easily determined. Although the method can be used for an unrestricted anisotropy, a special case of P, SV and SH plane waves, propagating in a plane of symmetry of a monoclinic (orthorhombic, hexagonal) viscoelastic medium is discussed in greater detail. In this plane the waves can be studied as functions of propagation direction N and of the real-valued inhomogeneity parameter D .F or inhomogeneous plane waves, D �= 0, and for homogeneous plane waves, D = 0. The use of the inhomogeneity parameter D offers many advantages in comparison with the conventionally used attenuation angle γ .I nthe N, D domain, any combination of N and D is physically acceptable. This is, however, not the case in the N, γ domain, where certain combinations of N and γ yield non-physical solutions. Another advantage of the use of inhomogeneity parameter D is the simplicity and universality of the algorithms in the N, D domain. Combined effects of attenuation and anisotropy, not known in viscoelastic isotropic media or purely elastic anisotropic media, are studied. It is shown that, in anisotropic viscoelastic media, the slowness vector and the related quantities are not symmetrical with respect to D = 0a s inisotropic viscoelastic media. The phase velocity of an inhomogeneous plane wave may be higher than the phase velocity of the relevant homogeneous plane wave, propagating in the same direction N. Similarly, the modulus of the attenuation vector of an inhomogeneous plane wave may be lower than that for the relevant homogeneous plane wave. The amplitudes of inhomogeneous plane waves in anisotropic viscoelastic media may increase exponentially in the direction of propagation N for certain D. The attenuation angle γ cannot exceed its boundary value, γ ∗ . The boundary attenuation angle γ ∗ is, in general, different from 90 ◦ , and depends both on the direction of propagation N and on the sign of the inhomogeneity parameter D. The polarization of P and SV plane waves is, in general, elliptical, both for homogeneous and inhomogeneous waves. Simple quantitative expressions or estimates for all these effects (and for many others) are presented. The results of the numerical treatment are presented in a companion paper (Paper II, this issue).

Nonlinear Alfvén waves, discontinuities, proton perpendicular acceleration, and magnetic holes/decreases in interplanetary space and the magnetosphere: intermediate shocks?

Abstract: . Alfven waves, discontinuities, proton perpendicular acceleration and magnetic decreases (MDs) in interplanetary space are shown to be interrelated. Discontinuities are the phase-steepened edges of Alfven waves. Magnetic decreases are caused by a diamagnetic effect from perpendicularly accelerated (to the magnetic field) protons. The ion acceleration is associated with the dissipation of phase-steepened Alfven waves, presumably through the Ponderomotive Force. Proton perpendicular heating, through instabilities, lead to the generation of both proton cyclotron waves and mirror mode structures. Electromagnetic and electrostatic electron waves are detected as well. The Alfven waves are thus found to be both dispersive and dissipative, conditions indicting that they may be intermediate shocks. The resultant "turbulence" created by the Alfven wave dissipation is quite complex. There are both propagating (waves) and nonpropagating (mirror mode structures and MDs) byproducts. Arguments are presented to indicate that similar processes associated with Alfven waves are occurring in the magnetosphere. In the magnetosphere, the "turbulence" is even further complicated by the damping of obliquely propagating proton cyclotron waves and the formation of electron holes, a form of solitary waves. Interplanetary Alfven waves are shown to rapidly phase-steepen at a distance of 1AU from the Sun. A steepening rate of ~35 times per wavelength is indicated by Cluster-ACE measurements. Interplanetary (reverse) shock compression of Alfven waves is noted to cause the rapid formation of MDs on the sunward side of corotating interaction regions (CIRs). Although much has been learned about the Alfven wave phase-steepening processfrom space plasma observations, many facets are still not understood. Several of these topics are discussed for the interested researcher. Computer simulations and theoretical developments will be particularly useful in making further progress in this exciting new area.

Optimization of acoustic mirrors for solidly mounted BAW resonators

Abstract: The overall performance of bulk acoustic wave (BAW) filters is dominated by the effective coupling coefficient and the quality factor of the constituting BAW resonators. Whereas the effective coupling coefficient and its dependency on the layer stack is quite accurately modeled with a simple one-dimensional acousto-electric model (e.g. Masonstransmission line model), the prediction and optimization of the resonators quality factor - particularly for solidly mounted resonators (SMR) - completely fails with this model: whereas a calculation of the acoustic reflectance of a standard quarter-wavelength mirror stack leads to theoretical Q-factors well above 10000, experimental SMR devices with this type of mirror show values of typically well below 1000. This discrepancy is commonly explained by either visco-elastic loss in the materials and/or laterally leaking waves leaving the active resonator area. However, we have found a new, far more important loss mechanism relating to shear waves generated in the device. These waves can be created by injection from the resonators border area as well as by reflection/refraction of longitudinal waves at non-perpendicular angle of incidence to a material interface. In this paper, a quantitative methodology for the optimization of the acoustic mirror layer stack will be proposed. The influence of the mirror structure on the trapping of both longitudinal and shear wave energy will be discussed based on this very simple approach. Trade-offs with respect to the other important device parameters, such as effective coupling coefficient, temperature coefficient of frequency (TCF) and purity of the electrical response, are analyzed. The usefulness of this approach for the optimization of resonator Q-values will be proven by experimental results demonstrating Q-factors of 1500 and higher.

Dynamics of the Solar Magnetic Network: Two-dimensional MHD Simulations

Abstract: The aim of this work is to identify the physical processes that occur in the network and contribute to its dynamics and heating. We model the network as consisting of individual flux tubes, each with a nonpotential field structure, that are located in intergranular lanes. With a typical horizontal size of about 150 km at the base of the photosphere, they expand upward and merge with their neighbors at a height of about 600 km. Above a height of approximately 1000 km the magnetic field starts to become uniform. Waves are excited in this medium by means of motions at the lower boundary. We focus on transverse driving, which generates both fast and slow waves within a flux tube and acoustic waves at the interface of the tube and the ambient medium. The acoustic waves at the interface are due to compression of the gas on one side of the flux tube and expansion on the other. These longitudinal waves are guided upward along field lines at the two sides of the flux tube, and their amplitude increases with height due to the density stratification. Being acoustic in nature, they produce a compression and significant shock heating of the plasma in the chromospheric part of the flux tube. For impulsive excitation with a time constant of 120 s, we find that a dominant feature of our simulations is the creation of vortical motions that propagate upward. We have identified an efficient mechanism for the generation of acoustic waves at the tube edge, which is a consequence of the sharp interface of the flux concentration. We examine some broad implications of our results.

Mode-selecting acoustic filter by using resonant tunneling of two-dimensional double phononic crystals

Abstract: In this letter, we investigated the resonant tunneling of elastic waves through double phononic potential barriers formed by two slabs of two-dimensional phononic crystals consisting of pure solid components. It is found that the resonant tunneling longitudinal waves can be distinguished easily from the resonant tunneling transverse waves. Thus, such double-barrier structures can be served as a mode-selecting acoustic filter, used to pick out the single longitudinal wave component or transverse wave component at a certain frequency.

The instability and breaking of long internal waves

Abstract: Laboratory experiments are carried out to determine the nature of internal wave breaking and the limiting wave steepness for progressive, periodic, lowest-mode internal waves in a two-layer, miscible density stratification. Shoaling effects are not considered. The waves investigated here are long relative to the thickness of the density interface separating the two fluid layers. Planar laser-induced fluoresence (PLIF) flow visualization shows that wave breaking most closely resembles a Kelvin–Helmholtz shear instability originating in the high-shear wave crest and trough regions. However, this instability is strongly temporally and spatially modified by the oscillations of the driving wave shear. Unlike a steady stratified shear layer, the wave instability discussed here is not governed by the canonical stability limit. Instead, the wave time scale (the time scale of the destabilizing shear) imposes an additional constraint on instability, lowering the critical Richardson number below 1/4. Experiments were carried out to quantify this instability threshold, and show that, for the range of wavenumbers considered in this study, the critical wave steepness at which the wave breaking occurs is wavenumber-dependent (unlike surface waves). The corresponding critical wave Richardson numbers at incipient wave breaking are well below 1/4, in consonance with a modified instability analysis based on results from stratified shear flow instability theory.

Gravity waves excited by jets: Propagation versus generation

Abstract: [1] Atmospheric jets are known to be an important source of inertia-gravity waves, yet remain poorly understood as such. Previous studies on the subject have concentrated on the generation mechanisms for the gravity waves, with the underlying assumption that the characteristics of the waves were imposed by the generation mechanism. In proceeding so, effects due to the propagation of the waves through a complex three-dimensional flow have been overlooked. Using numerical simulations of idealized baroclinic instability in a periodic channel, we show that propagation effects can determine several characteristics of the gravity waves emitted into the middle atmosphere from tropospheric jets. Specifically, the numerical simulations demonstrate that the propagation of inertia-gravity waves through horizontal deformation and vertical shear strongly influences the spatial organization of the waves and imposes the 3D orientation of their wave-vector.

Dynamics of the Solar Magnetic Network: Two-dimensional MHD Simulations

Abstract: The aim of this work is to identify the physical processes that occur in the network and contribute to its dynamics and heating. We model the network as consisting of individual flux tubes with a non-potential field structure that are located in intergranular lanes. With a typical horizontal size of 200 km at the base of the photosphere, they expand upward and merge with their neighbors at a height of about 600 km. Above a height of approximately 1000 km the magnetic field starts to become uniform. Waves are generated in this medium by means of motions at the lower boundary. We focus on transverse driving, which generates both fast and slow waves within a flux tube and acoustic waves at the interface of the tube and the field-free medium. The acoustic waves at the interface are due to compression of the gas on one side of the flux tube and expansion on the other. These waves travel upward along the two sides of the (2D) flux tube and enter it, where they become longitudinal waves. For impulsive excitation with a time constant of 120 s, we find that a dominant feature is the creation of vortical motions that propagate upward. We have identified an efficient mechanism for the generation of longitudinal waves and shock formation in the chromospheric part of the flux concentration. We examine some broad implications of our results.

Quantitative Estimation of Bone Density and Bone Quality Using Acoustic Parameters of Cancellous Bone for Fast and Slow Waves

Abstract: In previous studies, two longitudinal waves, the fast and slow waves, were observed in cancellous bone. The propagation speed of the fast wave increases with bone density and that of the slow wave remains almost constant. The attenuation constant of the fast wave is much higher than that of the slow wave and is independent of bone density, but the attenuation constant of the slow wave increases with bone density. In the present study, experimental results on ultrasonic waves transmitted through cancellous bone show that the fast wave amplitude increases proportionally and the slow wave amplitude decreases inversely with bone density. The dependence of the fast wave amplitude on bone density cannot be explained by the attenuation constant. The ultrasonic wave propagation path through cancellous bone is modeled to specify the causality between ultrasonic wave parameters and bone density. Then bone density and bone elasticity are quantitatively formulated.

Macrostructure of collisionless bow shocks: 1. Scale lengths

Abstract: [1] The global structure of collisionless bow shocks is investigated using a 2.5-dimensional electromagnetic hybrid code. This allows us to study the macrostructure of the shock while accounting for microphysical processes at the shock. The study entails the interaction of solar wind with magnetic dipoles of varying strength. For very weak dipoles the interaction does not lead to formation of a shock since the obstacle is not strong enough for the flow to become subsonic. For lager dipole strengths, a bow shock/wave is formed due to the presence of a plasma stagnation region in front of the dipole. It is found that the quasi-perpendicular part of this boundary corresponds to a true shock wave, whereas the quasi-parallel side consists of a magnetosonic wave followed by a rotational discontinuity. The backstreaming ions in the foreshock of this interaction lead to the generation of parallel propagating sinusoidal waves. These waves result in beam scattering, however, do not affect the solar wind. The formation of quasi-parallel shock is tightly connected to the generation of oblique compressional waves. These waves are generated by backstreaming ions having a beam-ring distribution function and are an inherent part of the shock dissipation processes. The results demonstrate that the two classes of 30 s ULF waves observed in the ion foreshock are unrelated. The results also demonstrate that at least in 2.5-dimensional, plasma scales determine the nature of the bow shock to a large extent although system size can influence both particle acceleration and evolution of ULF waves.

Simulation of ultrasound propagation through bovine cancellous bone using elastic and Biot's finite-difference time-domain methods.

Abstract: The propagation of ultrasonic pulse waves in bovine cancellous bone has been numerically analyzed in two dimensions by using two finite-difference time-domain (FDTD) methods: the commonly used elastic FDTD method and an FDTD method extended with Biot’s theory for a porous elastic solid saturated with viscous fluid. Both FDTD results were compared with the results of previous experiments by Hosokawa and Otani [J. Acoust. Soc. Am. 101, 558–562 (1997)], in which the Biot’s fast and slow longitudinal waves were clearly identified. It was difficult to analyze both the fast and slow waves with the elastic FDTD method because of the inadequate 2D model of cancellous bone. On the other hand, in Biot’s FDTD results that consider the pore fluid motion relative to the solid frame, both waves could be clearly observed. The experimental and simulated values of the speeds of these waves were in good agreement. Using the modified Biot’s FDTD equations containing the possible attenuations for the fast wave other than the...

On the generation of solitary waves observed by Cluster in the near-Earth magnetosheath

Abstract: Through case studies involving Cluster waveform observations, solitary waves in the form of bipolar and tripolar pulses have recently been found to be quite abundant in the near-Earth dayside magnetosheath. We expand on the results of those previous studies by examining the distribution of solitary waves from the bow shock to the magnetopause using Cluster waveform data. Cluster's orbit allows for the measurement of solitary waves in the magnetosheath from about 10 RE to 19.5 RE. Our results clearly show that within the magnetosheath, solitary waves are likely to be observed at any distance from the bow shock and that this distance has no dependence on the time durations and amplitudes of the solitary waves. In addition we have found that these same two quantities show no dependence on either the ion velocity or the angle between the ion velocity and the local magnetic field direction. These results point to the conclusion that the solitary waves are probably created locally in the magnetosheath at multiple locations, and that the generation mechanism is most likely not solely related to ion dynamics, if at all. To gain insight into a possible local generation mechanism, we have examined the electron differential energy flux characteristics parallel and perpendicular to the magnetic field, as well as the local electron plasma and cyclotron frequencies and the type of bow shock that Cluster is behind, for several time intervals where solitary waves were observed in the magnetosheath. We have found that solitary waves are most likely to be observed when there are counterstreaming (~parallel and anti-parallel to the magnetic field) electrons at or below about 100eV. However, there are times when these counterstreaming electrons are present when solitary waves are not. During these times the background magnetic field strength is usually very low (<10nT), implying that the amplitudes of the solitary waves, if present, would be near or below those of other waves and electrostatic fluctuations in this region making it impossible to isolate or clearly distinguish them from these other emissions in the waveform data. Based on these results, we have concluded that some of the near-Earth magnetosheath solitary waves, perhaps in the form of electron phase-space holes, may be generated locally by a two-stream instability involving electrons based on the counterstreaming electrons that are often observed when solitary waves are present. We have not ruled out the possibility that the solitary waves could be generated as a result of the lower-hybrid Buneman instability in the presence of an electron beam, through the electron acoustic mode or through processes involving turbulence, which is almost always present in the magnetosheath, but these will be examined in a more comprehensive study in the future.

Transit-time instability in Hall thrusters

Abstract: Longitudinal waves characterized by a phase velocity of the order of the velocity of ions have been recurrently observed in Hall thruster experiments and simulations. The origin of this so-called ion transit-time instability is investigated with a simple one-dimensional fluid model of a Hall thruster discharge in which cold ions are accelerated between two electrodes within a quasineutral plasma. A short-wave asymptotics applied to linearized equations shows that plasma perturbations in such a device consist of quasineutral ion acoustic waves superimposed on a background standing wave generated by discharge current oscillations. Under adequate circumstances and, in particular, at high ionization levels, acoustic waves are amplified as they propagate, inducing strong perturbation of the ion density and velocity. Responding to the subsequent perturbation of the column resistivity, the discharge current generates a standing wave, the reflection of which sustains the generation of acoustic waves at the inlet boundary. A calculation of the frequency and growth rate of this resonance mechanism for a supersonic ion flow is proposed, which illustrates the influence of the ionization degree on their onset and the approximate scaling of the frequency with the ion transit time. Consistent with experimental reports, the traveling wave can be observed on plasma density and velocity perturbations, while the plasma potential ostensibly oscillates in phase along the discharge.

Frictional sliding modes along an interface between identical elastic plates subject to shear impact loading

Abstract: Frictional sliding along an interface between two identical isotropic elastic plates under impact shear loading is investigated experimentally and numerically. The plates are held together by a compressive stress and one plate is subject to edge impact near the interface. The experiments exhibit both a crack-like and a pulse-like mode of sliding. Plane stress finite element calculations modeling the experimental configuration are carried out, with the interface characterized by a rate and state dependent frictional law. A variety of sliding modes are obtained in the calculations depending on the impact velocity, the initial compressive stress and the values of interface variables. For low values of the initial compressive stress and impact velocity, sliding occurs in a crack-like mode. For higher values of the initial compressive stress and/or impact velocity, sliding takes place in a pulse-like mode. One pulse-like mode involves well-separated pulses with the pulse amplitude increasing with propagation distance. Another pulse-like mode involves a pulse train of essentially constant amplitude. The propagation speed of the leading pulse (or of the tip of the crack-like sliding region) is near the longitudinal wave speed and never less than √2 times the shear wave speed. Supersonic trailing pulses are seen both experimentally and computationally. The trends in the calculations are compared with those seen in the experiments.