Non-dispersive Wave Research Articles

Experiments and molecular-dynamics simulation of elastic waves in a plasma crystal radiated from a small dipole source.

The radiation of elastic waves from a localized source is observed experimentally in a two-dimensional plasma crystal. An initial shear stress applied by a laser forms a small dipole source. The emerging complex wave pattern is shown to consist of outgoing compressional and shear wave pulses. Subsequent structures are identified as inward-going waves due to the finite size of the source region, which reappear on the opposite side. The compressional wave forms a trailing wave train due to strong dispersion, while the nondispersive shear wave evolves into a vortex-antivortex pair on either side. The experiments are compared with a molecular-dynamics simulation.

Acoustic Noise-Source Identification in Aircraft-Based Atmospheric Temperature Measurements

Atmospheric temperature fluctuation data collected from a Grumman Gulfstream II aircraft show features in temperature power spectral density functions that do not follow the expected - 5/3 slope for homogeneous isotropic turbulence. Spectral analysis techniques show that these features result from the upstream propagation of a nondispersive acoustical wave. The source of the acoustical wave, which appears only at flight altitudes greater than 28,000 ft (8530 m), is attributed to engine acoustics in the form of jet screech where vortical structures interact with a quasi-periodic shock cell structure, both in the jet exhaust. The nature of the acoustical disturbance is shown to be dependent on velocity, with increased velocity resulting in a decrease in jet-screech peak frequency. These results are found to be consistent with those of other researchers investigating jet screech in jet flows.

Equatorial Deep Jets and Abyssal Mixing in the Indian Ocean

Vertical profiles of horizontal currents and hydrographic measurements from three cruises along 80.58E from the coast of Sri Lanka to 68S between December 1990 and September 1994 are used to investigate the scales of the Indian Ocean deep jets as well as internal wave parameters and dissipation at the equator. The deep jets at 80.58E have a vertical wavelength of 660 sm (stretched meters) and amplitudes exceeding 10 cm s21 in zonal velocity. They are observed throughout the water column and their flow direction reverses at 2 8 off the equator. The vertical positions of the jets differ among the cruises and are consistent with a flow reversal between the data collected in winter and summer. During September 1994, the jets were less pronounced. Due to the meridional distribution of their zonal velocity and the phase relationship between zonal velocity and vertical displacement, the jets are best described as nondispersive first-mode equatorial Rossby waves. The hydrographic data revealed thick layers of low stratification with vertical scales of 15‐55 m in the upper 2000 m of the water column. They are found primarily within 18 of the equator and there is some evidence of correlation between the vertical position as well as the extent and the high strain zones of the deep jets. At vertical wavenumbers larger than those of the deep jets, shear and strain levels are five times larger than at off-equatorial locations and the compliant internal wave range (‘‘roll-off range’’) begins at a smaller wavenumber ( kc 0.02 cpsm). An estimate of the average dissipation rate within the deep jets yielded 5 7.5 3 10210 Wk g 21 between 500- and 2000e m depth. The elevated finescale internal wave field appears to be the main cause for the existence of the low stratification layers.

Nonlinear Dispersion of Surface Gravity Waves in Shallow Water*

The nonlinear dispersion of random, directionally spread surface gravity waves in shallow water is examined with Boussinesq theory and field observations. A theoretical dispersion relationship giving a directionally averaged wavenumber magnitude as a function of frequency, the local water depth, and the local wave spectrum and bispectrum is derived for waves propagating over a gently sloping beach with straight and parallel depth contours. The linear, nondispersive shallow water relation is recovered as the first-order solution, with weak frequency and amplitude dispersion appearing as second-order corrections. Wavenumbers were estimated using four arrays of pressure sensors deployed in 2‐6-m depth on a gently sloping sandy beach. When wave energy is low, the observed wavenumbers agree with the linear, finitedepth dispersion relation over a wide frequency range. In high energy conditions, the observed wavenumbers deviate from the linear dispersion relation by as much as 20%‐30% in the frequency range from two to three times the frequency of the primary spectral peak, but agree well with the nonlinear Boussinesq dispersion relation, confirming that the deviations from linear theory are finite amplitude effects. In high energy conditions, the predicted frequency and amplitude dispersion tend to cancel, yielding a nearly nondispersive wave field in which waves of all frequencies travel with approximately the linear shallow water wave speed, consistent with the observations. The nonlinear Boussinesq theory wavenumber predictions (based on the assumption of irrotational wave motion) are accurate even within the surf zone, suggesting that wave breaking on gently sloping beaches has little effect on the dispersion relation.

Resonant Triads Involving a Nondispersive Wave

A simple system is studied, involving a single nondispersive breaking wave and its interaction with two dispersive modes through a resonant triad. The dynamics of this system are shown to be quite rich, through a combined theoretical and numerical analysis. A sharply defined traveling wave with a corner seems to attract almost all initial data with enough energy, provided the nondispersive wave is unstable to the other two when standing alone. In other cases, the solution converges to quasiperiodic final states, unless extra symmetries force the solution to converge to simpler configurations.

Investigation of frictional properties of lubricants at transient elastohydrodynamic conditions

In the assessment of lubricant properties and in various contact applications, it is of importance to know the frictional qualities. Under quasi-static conditions, normal and transverse forces are measured using force transducers but the task is more difficult when loads are high and transient, as they often are in elastohydrodynamic conjunctions. The experimental method presented in this paper is based on analysis of propagating waves in a beam, due to an impact on its end surface, using FFT analysis. Since the impact is oblique, both non-dispersive compression waves and dispersive flexural waves are generated. The normal force originating from the axial wave is measured using straingauges, while the transverse force is derived from the FFT's of two lateral acceleration histories using Euler–Bernoulli dynamic beam theory. The relation between normal- and transverse force histories displays the frictional properties at the impact as a function of time, i.e. variations in frictional properties during loading and unloading (typically 200–400 μs in ball bearings and gears) can be observed. A variety of lubricants have been studied up to a Hertzian pressure of 2.5 GPa, and the method and results are presented.

Fermat’s principle and acoustic tomography in a time-dependent ocean

Fermat’s principle states that, for nondispersive waves propagating between two given points, travel time is stationary with respect to small variations of the wave propagation path around the actual path (i.e., ray) taken by the wave. This fundamental principle governing short wave kinematics was first established by seventeenth century French mathematician Pierre de Fermat. The principle is of particular importance for acoustic tomography because it allows one to neglect perturbations in ray geometry when performing a linear inversion of acoustic travel times for sound speed variations. Derivations of Fermat’s principle available in the literature does not apply to acoustic waves in media with time-dependent sound speed. Moreover, the very formulation of the principle in this case is not obvious as travel time along a trial ray ceases to be a single-valued functional of the trial ray geometry. In this paper, the Fermat’s principle is extended to media with time-dependent parameters. We consider acoustic waves in the inhomogeneous, moving or quiescent fluid. Formulations of the principle in terms of travel time and eikonal are compared. Applications of the established principle to ocean acoustic tomography and modeling wave propagation in weakly nonstationary, inhomogeneous ocean are discussed. [Work supported by ONR.]

Electronically tunable nondispersive magnetostaticwave delay line

An electronically tunable, nondispersive magnetostatic wave delay line consisting of cascaded magnetostatic backward volume waves and magnetostatic surface waves delay lines has been designed and realised. The distinguishing feature of the device is a wide continuously tunable time delay range of ±30% with the central value of 58 ns. An obtained bandwidth for constant time delay is ~300 MHz at a 3.15 GHz centre frequency. A deviation from constant delay is < ±5%.

Impulse propagation in dissipative and disordered chains with power-law repulsive potentials

We report particle dynamics based studies of impulse propagation in a chain of elastic beads with dissipative contacts and with randomly distributed masses. The interaction between the beads is characterized by the potential V( δ)∼ δ n , δ≥0 being grain overlap, n>2 and at zero external loading, i.e., under conditions of “sonic vacuum” in which sound cannot propagate through the chain [J. Appl. Mech. Technol. Phys. 5 (1983) 733]. In the earlier work, we have confirmed the studies of Nesterenko and coworkers and have reported that impulses propagate as solitary waves in the system of interest in the absence of dissipation and disorder [Physica A 268 (1999) 644]. In the present study, we first discuss the effects of restitution and velocity dependent friction on the propagation of the impulse. We next report that the maximum energy E max of the solitary wave as it propagates from a chain of monodisperse grains of mass m to a chain with masses m(1+ r( z) ϵ), where −1≤ r( z)≤1 and ϵ=const. that measures the degree of randomness, decays with linear distance traveled z as exp(− α E z), α E ∼ ϵ 2+ f( n) , f( n) being some n dependent constant for 2< n<∞. In monodisperse chains, the velocity of the solitary wave c∼ E max ( n−2)/2 n . In polydisperse chains, we show that the propagation speed of a non-dispersive solitary wave decays with distance as exp(− α c z), where α c = α E ( n−2)/2 n.

Properties of a Monolithic Electroacoustic Device Geometry Using GaAs Resonant Tunnelling Structures

We present experimental and theoretical work on a monolithic electroacoustic system which exploits the interaction between a 1 GHz surface acoustic wave and electrons in a GaAs-AlGaAs resonant tunnelling structure. Non-annealed Ohmic contacts using in situ grown Al are employed to obtain stable dc operation. The microwave response of the system is explained, with features attributed to charge accumulation in the spacer layer adjacent to the quantum well. The influence of screening of the surface acoustic wave potential by the highly-doped substrate is also investigated, showing the need for a wide depletion layer. Potential applications for this system in signal processing and power microwave devices are discussed, along with a suggested mechanism for a non-dispersive surface acoustic wave transducer which relies on the nonlinear properties of the system.

The wave energy in nonlinearly deformable composites

The energy characteristics of waves propagating in composites are discussed. To describe the deformation of materials, two models are used — the classical model of an elastic body and the microstructural model of a two-phase elastic mixture. Both models take into account the quadratic nonlinearity of deformation based on the Murnaghan elastic potential. Analytical expressions for the velocity at which the energy of travelling plane longitudinal waves propagates are derived. It is shown that the nonlinearity of composite deformation decreases the velocities of energy propagation of both nondispersive and dispersive waves

Approximate particle-like solutions for a nonlinear relativistic scalar complex field model in 3+1 dimensions

A weakly nonlinear Lorentz invariant complex field model in 3+1 dimensions is studied by an asymptotic perturbation method, based on Fourier expansion and spatio-temporal rescaling. It is shown that a nonlinear system of partial differential equations describes oscillation amplitudes of Fourier modes. This system is C-integrable, i.e., can be linearized through a suitable transformation of the dependent and independent variables. We resolve the Cauchy problem and demonstrate that localized nondispersive waves (envelope solitons) with finite energy exist under appropriate initial conditions. These particle-like solutions propagate with the group velocity of their carrier wave. During a collision solitons maintain their shape, because the only change is a phase shift. Energy E and momentum p of solitons are identical to those of a relativistic particle. If the Planck constant is connected to the spatial dimension of the envelope soliton, then we obtain at the lowest order of approximation the quantum relations E=ℏ ω, λ= h/ p, where λ and ω are wavelength and frequency of the carrier wave. This work represents a possible way to achieve the Einstein–de Broglie soliton–particle concept.

THE TRANSMISSION CHARACTERISTICS OF THE ELASTIC SHEAR WAVE AT A SEMI-INFINITE EFFECTIVE CHIRAL MEDIUM

The plane wave propagating in effective chiral (isotropic, non-centrosymmetric) materials had been asymptotically investigated. They can be constructed by embedding structural chiral microstructures in a host medium, and six independent wavenumbers can hence be observed from the dispersion equations. Two of the wavenumbers represent the non-dispersive longitudinal waves while the remaining four represent the dispersive circularly polarized shear waves. The dispersion equations also indicate that two transition frequencies divide the frequency spectrum of the transverse wavenumbers into three different groups and the four transverse mode can only be distinguished in a specified frequency range. To continue our previous research, the field equations governing the harmonic motions at the achiral–chiral interface are written as a matrix form to solve the reflected and transmitted wave fields. Numerical results show that the P-, SV-, and SH-waves are coupled together when an elastic shear wave is incident at the achiral–chiral interface. Meanwhile, the two coupled transverse waves, i.e., the LCP and RCP plane waves, will degenerate to a linearly transverse plane wave when the shear wave is incident normally. The phenomenon may explain why the mode conversion due to the chirality is particularly enhanced between the first and second transition frequencies.

Wave propagation in thin Plexiglas plates: implications for Rayleigh waves

Two-dimensional (2D) experimental models are often used to study wave propagation problems. The advantages of using 2D experimental models, as opposed to 3D models, is the reduction of both extraneous reflections and mathematical complexity. Further, many structural elements conform to this geometry. The following study examines Rayleigh wave motion in thin Plexiglas sheets. Source–receiver time domain measurements were made at different locations on the Plexiglas sheet. The time–distance space was 2D-Fourier transformed into the frequency–wavenumber space to facilitate the analysis of wave modes propagating in the Plexiglas sheet. Experimental results showed that fundamental symmetric (S 0) and antisymmetric (A 0) Lamb waves propagated through the plate. Along the thickness of the plate, a non-dispersive Rayleigh wave was generated. Lamb waves were found to interfere with the Rayleigh wave. The assumption of generalized plane stress is preserved if higher mode Lamb waves have low energy content.

Resonant acceleration and heating of solar wind ions by dispersive ion cyclotron waves

We investigate the preferential acceleration and heating of solar wind alpha particles by the resonant cyclotron interaction with parallel‐propagating left‐hand‐polarized ion cyclotron waves. The Alfvén wave spectrum equation is generalized to multi‐ion plasmas and a Kolmogorov type of cascade effect is introduced to transfer energy from the low‐frequency Alfvén waves to the high‐frequency ion cyclotron waves, which are assumed to be entirely dissipated by the wave‐particle interaction. In order to distribute the dissipated wave energy among the alphas and protons, the quasi‐linear theory of the wave‐particle interaction is used along with the cold plasma dispersion relation, and a power law spectrum of the ion cyclotron waves is assumed, with the spectral index as a free parameter of the model. The set of three‐fluid solar wind equations and the Alfvén wave spectrum equation are then solved in order to find fast solar wind solutions. It is found that the effect of the alpha particles on the dispersion relation, omitted in most previous wave‐driven solar wind models, has a significant influence on the preferential acceleration and heating of the alphas, especially in the region close to the Sun. With this effect included, the alpha particles can be accelerated to a bulk flow speed faster than the protons by a few hundred kilometers per second and heated by the resonant cyclotron interaction to more than mass‐proportional temperature values at several solar radii. However, this mechanism does not yield a differential speed of the order of an Alfvén speed and a mass‐proportional temperature for the alphas beyond 0.3 AU, as observed, which confirms the same conclusion reached previously by Isenberg and Hollweg [1983] for nondispersive ion cyclotron waves.

A reduced model for nonlinear dispersive waves in a rotating environment

The simplest model for geophysical flows is one layer of a constant density fluid with a free surface, where the fluid motions occur on a scale in which the Coriolis force is significant. In the linear shallow water limit, there are non-dispersive Kelvin waves, localized near a boundary or near the equator, and a large family of dispersive waves. We study weakly nonlinear and finite depth corrections to these waves, and derive a reduced system of equations governing the flow. For this system we find approximate solitary Kelvin waves, both for waves traveling along a boundary and along the equator. These waves induce jets perpendicular to their direction of propagation, which may have a role in mixing. We also derive an equivalent reduced system for the evolution of perturbations to a mean geostrophic flow.

Wavenumber‐frequency structure of infragravity swash motions

Alongshore‐separated time series of natural swash motions were obtained over a range of environmental conditions using a video technique. Although the frequency spectra and normalized wavenumber spectra for these motions were particularly bland, wavenumber‐frequency spectra of these data showed clear partitions of infragravity band energy levels associated with various wave types. For the frequencies 0.025 &lt; ƒ ≤ 0.05 Hz, 45 ± 13% of the shoreline variance was, on average, associated with high‐mode (n ≥ 2) edge waves and/or leaky waves, while approximately half that amount was associated with low‐mode edge waves. Gravity wave motions (comprising both edge and leaky modes) were typically dominant in a lower‐frequency band (0.001 &lt; ƒ ≤ 0.025 Hz). A substantial portion of the variance in this band (21 ± 10%, with a maximum of 38%), however, was identified as a nondispersive waveform with wavenumbers well outside of the wavenumber‐frequency bounds for gravity waves. Surprisingly, this nongravity swash variance showed no significant dependence on mean alongshore current strength or mean alongshore current shear as measured in the surf zone trough separating the shoreline from an offshore bar. In addition, the celerities of these swash zone nondispersive waves were found to differ in magnitude, and in one instance, sign, from celerities of similarly structured waves measured farther offshore in the surf zone. These unexpected observations with respect to low‐frequency, nongravity swash energy imply a strong decorrelation between trough and shoreline fluid motions.

METHOD FOR INVESTIGATION OF FRICTIONAL PROPERTIES AT IMPACT LOADING

In the assessment of lubricant performance and also in various other contact applications it is of importance to know the frictional qualities of a surface. Under quasi-static conditions, normal and frictional forces are measured using force transducers but the task is more difficult when loads are transient. The experimental method presented in this paper is based on the analysis of propagating waves in a beam, due to an impact on the end surface. The impact is oblique and therefore a transverse as well as a normal force is generated. The normal force history is measured from the axial non-dispersive wave using strain gauges. Transverse force and bending moment both generate dispersive flexural waves. From the FFT of two transverse acceleration histories, the frictional force at the end of the rod is evaluated using beam theory. The relation between normal and frictional force histories displays the frictional properties at the impact. Preliminary results are presented.

Nondispersive magnetostatic forward volume wave propagation in a double-layered yttrium–iron–garnet film structure with dielectric spacer

The present article reports a theoretical study of nondispersive magnetostatic forward volume wave (MSFVW) propagation in a double-layered yttrium–iron–garnet (YIG)-film structure consisting of two YIG films separated by a dielectric layer. Numerical computations are presented that show that a significant improvement in bandwidth for nondispersive MSFVW propagation can be obtained in the present separated double-layered YIG-film structure over the previously reported double-layered YIG-film geometry wherein the two YIG films were in direct contact.

The influence of the mass matrix on the dispersive nature of the semi-discrete, second-order wave equation

The application of discrete solution methods to the second-order wave equation can yield a dispersive representation of the non-dispersive wave propagation problem resulting in a phase speed that depends, not only upon the wavelength of the signal being propagated, but also upon the direction of propagation. In this work, the dependence of the dispersive errors on the wave propagation direction, mesh aspect ratio and wave number is investigated with the goal of understanding and hopefully reducing the phase and group errors associated with the two-dimensional bilinear finite element. An analysis of the dispersive effects associated with the consistent, row—sum lumped and higher-order mass matrices has led to a reduced-coupling ‘penta-diagonal’ mass matrix that yields improved phase and group errors with respect to wavelength and propagation direction. The influence of row—sum lumping the finite element mass matrix is demonstrated to always introduce lagging phase and group error, while a linear combination of the lumped and consistent mass matrices, i.e. a higher-order mass matrix, is shown to improve the dispersion characteristics of both the reduced and full-integration element. Using a 2.5% phase error metric, the higher-order mass matrix can reduce the mesh resolution requirements relative to the lumped mass matrix by nearly a factor of two in one dimension; a factor of 4 in two dimensions. Similarly, the reduced-coupling mass matrix can reduce the grid requirements by a factor of approximately four relative to the lumped mass matrix; a factor of 16 in two dimensions. Although the reduced-coupling mass matrix requires additional storage relative to the lumped mass, the factor of 16 reduction in grid requirements promises tremendous overall savings for computing a fixed wavelength spectrum, or alternatively for resolving shorter wavelengths with a fixed grid resolution.