Showing papers on "Longitudinal wave published in 2002"

Ocean waves and oscillating systems : linear interactions including wave-energy extraction

Abstract: 1. Introduction 2. Mathematical description of oscillations 3. Interaction between oscillations and waves 4. Gravity waves on water 5. Wave-body interactions 6. Wave-energy absorption by oscillating bodies 7. Wave interactions with oscillating water columns Bibliography Index.

Magnetoinductive waves in one, two, and three dimensions

Abstract: The propagation of waves supported by capacitively loaded loops is investigated using a circuit model in which each loop is coupled magnetically to a number of other loops. Since the coupling is due to induced voltages the waves are referred to as magnetoinductive (MI) waves. The mathematical formulations are mostly analytical thanks to long standing previous work on the magnetic and electric fields generated by currents flowing in loops. Retardation is neglected, i.e., dimensions of the structure are assumed to be small relative to the free space wavelength. The dispersion relations, derived in the most general case for a tetragonal three-dimensional structure, exhibit both forward and backward waves within a pass band. It is shown that for reproducing the salient features of the waves it is sufficient to take nearest neighbor coupling into account but coupling between loops further away must also be considered if higher accuracy is required. The investigations include that of resonances, conditions for the existence of traveling waves, tolerances, and streamlines of the Poynting vector. Waveguide components, like bends, power dividers and couplers are considered due to the potential applications of the MI waves as magnetic guides. Generality of the results, their possible implications for transverse electromagnetic wave propagation, previous work on similar waves, including the possibility of phase conjugation, are discussed in a separate section.

Complex Wave Dynamics on Thin Films

Abstract: Formulation and Linear Orr-Sommerfeld Theory: Navier-Stokes Equation with interfacial conditions Linear stability of the trivial solution to two- and three-dimensional perturbations Longwave expansion for surface waves Unusual case of zero surface tension Surface waves - Numerical solution of the Orr-Sommerfeld equations. Hierarchy of Model Equations: Kuramoto-Sivashinsky (KS), KdV and related weakly nonlinear equations Lubrication theory to derive Benney's longwave equation Depth-averaged integral equations Combination of Galerkin-Petrov method with weighted residuals Validity of the equations Spatial and temporal primary instability of the Shkadov model. Experiments and Numerical Simulation: Experiments on falling-film wave dynamics Numerical formulation Numerical simulation of noise-driven wave transitions Pulse formation and coarsening. Periodic and Solitary Wave Families: Main properties of weakly nonlinear waves in an active/dissipative medium Phase space of stationary KS equation Solitary waves and Shilnikov theorem Bifurcations of spatially periodic travelling waves and their stability Normal Form analysis for the Kawahara equation Nonlinear waves far from criticality - the Shkadov model Stationary waves of the boundary layer equation and Shkadov model Navier-Stokes equation of motion - the effects of surface tension. Floquet Theory and Selection of periodic Waves: Stability and selection of stationary waves Stable intervals from a Coherent Structure Theory Evolution towards solitary waves. Spectral Theory for gKS Solitary Pulses: Pulse spectra Some numerical recipes to construct eigenfunctions and obtain spectra Stability of gKS pulses Attenuation of radiation wave packet by stable pulses Resonance pole-a discrete culmination of the continuous spectrum Resonance pole description of mass drainage Suppression of wave packets by a periodic train of pulses. (Part contents).

Elastic waves in bodies with initial (residual) stresses

Abstract: An analysis is made of the results obtained in the three-dimensional linearized theory of elastic waves propagating in initially stressed solids. Consideration is given to surface waves along planar and curvilinear boundaries and interfaces, waves in layers and cylinders, waves in composite materials, waves in hydroelastic systems, and dynamic problems for moving loads. The results were obtained in exact formulations.

Generalized plasma dispersion function for a plasma with a kappa-Maxwellian velocity distribution

Abstract: A generalized plasma dispersion function has previously been obtained for waves in plasmas with isotropic kappa distributions for arbitrary real kappa [Mace and Hellberg, Phys Plasmas 2, 2098 (1995)] In many instances plasmas are found to have anisotropic power-law distributions, and hence a similar dispersion function for electrostatic waves in plasmas having a one-dimensional kappa distribution along a preferred direction in space, and a Maxwellian distribution perpendicular to it has now been developed It is used to study the effect of superthermal electrons and ions on ion-acoustic waves propagating at an angle to a magnetic field This dispersion function should find application to wave studies both in space plasmas, where the magnetic field defines a preferred direction, and in dusty plasma crystal studies, where the ion flow direction is unique

Guided ultrasonic waves in long bones: modelling, experiment and in vivo application

Abstract: Existing ultrasound devices for assessing the human tibia are based on detecting the first arriving signal, corresponding to a wave propagating at, or close to, the bulk longitudinal velocity in bone. However, human long bones are effectively irregular hollow tubes and should theoretically support the propagation of more complex guided modes similar to Lamb waves in plates. Guided waves are attractive because they propagate throughout the bone thickness and can potentially yield more information on bone material properties and architecture. In this study, Lamb wave theory and numerical simulations of wave propagation were used to gain insights into the expected behaviour of guided waves in bone. Experimental measurements in acrylic plates, using a prototype low-frequency axial pulse transmission device, confirmed the presence of two distinct propagating waves: the first arriving wave propagating at, or close to, the longitudinal velocity, and a slower second wave whose behaviour was consistent with the lowest order Lamb antisymmetrical (A0) mode. In a pilot study of healthy and osteoporotic subjects, the velocity of the second wave differed significantly between the two groups, whereas the first arriving wave velocity did not, suggesting the former to be a more sensitive indicator of osteoporosis. We conclude that guided wave measurements may offer an enhanced approach to the ultrasonic characterization of long bones.

Full waveform numerical simulations of seismoelectromagnetic wave conversions in fluid‐saturated stratified porous media

Abstract: [1] We present a full-waveform modeling technique of the coupled seismoelectromagnetic wave propagation in fluid-saturated stratified porous media. Our simulation code uses the macroscopic governing equations derived by Pride [1994], which couple Biot's theory and Maxwell equations via flux/force transport equations. In this theory the coupling mechanism is explained by electrokinetic effects taking place at the pore level. The synthetic seismoelectrograms and seismomagnetrograms are computed by extending the generalized reflection and transmission matrix method and by using a discrete wave number integration of the global reflectivity obtained in the frequency wave number domain. Synthetic time sections and snapshots of the wave propagation are used to study the seismic, electromagnetic, and seismoelectromagnetic waves properties in fluid-saturated layered porous media. Two wave phenomena are investigated: (1) the electric and magnetic fields induced by the propagation of a seismic perturbation in a homogeneous porous medium and (2) the electromagnetic waves generated at depth when seismic waves propagate through a vertically heterogeneous porous medium. Concentrating on the second effect, we show that the zone which effectively contributes to the generation of EM disturbances along a plane interface coincides with the first Fresnel zone associated with a seismic-to-electromagnetic wave conversion. A numerical sensitivity study shows that the EM waves generated at depth by the passage of seismic waves through an interface are particularly sensitive to contrasts in porosity, permeability, fluid salinity, and fluid viscosity. Our numerical simulations highlight the potential of artificially generated seismoelectromagnetic converted waves for the characterization of the subsurface and its fluid content.

A numerical investigation of solitary internal waves with trapped cores formed via shoaling

Abstract: The formation of solitary internal waves with trapped cores via shoaling is investigated numerically. For density fields for which the buoyancy frequency increases monotonically towards the surface, sufficiently large solitary waves break as they shoal and form solitary-like waves with trapped fluid cores. Properties of large-amplitude waves are shown to be sensitive to the near-surface stratification. For the monotonic stratifications considered, waves with open streamlines are limited in amplitude by the breaking limit (maximum horizontal velocity equals wave propagation speed). When an exponential density stratification is modified to include a thin surface mixed layer, wave amplitudes are limited by the conjugate flow limit, in which case waves become long and horizontally uniform in the centre. The maximum horizontal velocity in the limiting wave is much less than the wave's propagation speed and as a consequence, waves with trapped cores are not formed in the presence of the surface mixed layer.

Monochromatic and random wave breaking at blocking points

Abstract: [1] In this paper we study the energy dissipation due to current-limited wave breaking in monochromatic and random waves with the help of experimental tests. The opposing currents are strong enough for wave blocking to occur. A modified bore model is used to simulate the dissipation rate in the monochromatic waves, and an empirical bulk dissipation formula for wave breaking in random waves is proposed. The effects of wave blocking on the dynamics of the wave field are also discussed. INDEX TERMS: 4546 Oceanography: Physical: Nearshore processes; 4560 Oceanography: Physical: Surface waves and tides (1255); 4512 Oceanography: Physical: Currents; 4528 Oceanography: Physical: Fronts and jets; KEYWORDS: wave-current interaction, wave breaking, wave action conservation, nonlinear dispersion, inlets

Modelling of short wave diffraction problems using approximating systems of plane waves

Abstract: This paper describes a finite element model for the solution of Helmholtz problems at higher frequencies that offers the possibility of computing many wavelengths in a single finite element. The approach is based on partition of unity isoparametric elements. At each finite element node the potential is expanded in a discrete series of planar waves, each propagating at a specified angle. These angles can be uniformly distributed or may be carefully chosen. They can also be the same for all nodes of the studied mesh or may vary from one node to another. The implemented approach is used to solve a few practical problems such as the diffraction of plane waves by cylinders and spheres. The wave number is increased and the mesh remains unchanged until a single finite element contains many wavelengths in each spatial direction and therefore the dimension of the whole problem is greatly reduced. Issues related to the integration and the conditioning are also discussed.

Dispersion relations of longitudinal and transverse waves in two-dimensional screened Coulomb crystals.

Abstract: Dispersion relations of longitudinal and transverse waves in two-dimensional (2D) screened-Coulomb crystals were investigated. The waves were excited in 2D crystals made from complex plasmas, i.e., dusty plasmas, by applying radiation pressure of laser light. The dependencies of the dispersion relation on the shielding parameter, the damping rate, and the wave propagation direction were experimentally measured. The measured dispersion relations agree reasonably with a recently developed theory, and the comparison yields the shielding parameter and the charge on particles.

Surface Acoustic Waves in Materials Science

Abstract: Laser-generated surface waves provide new tools for studying material properties, from linear elastic behavior to fracture.

Stability of Hypersonic Boundary Layers over a Compression Corner

Abstract: The stability of hypersonic boundary layers over a compression corner is investigated numerically. To compute the shock and the interaction of the shock with the instability waves, the simulation solves the three-dimensional Navier-Stokes equations using a high-order, weighted, essentially nonoscillatory shock-capturing scheme. After computing the mean flowfield, the procedure then superimposes two-dimensional unsteady disturbances at the inflow and computes the evolution of these disturbances in downstream direction. Because of the interaction of the shock with the boundary layer, a separation bubble forms at the corner, and two compression waves form near the separation and reattachment points. These compression waves merge farther away from the boundary layer to form a shock

Long-wave forcing by the breaking of random gravity waves on a beach

Abstract: This paper presents new laboratory data on long-wave (surf-beat) forcing by the random breaking of shorter gravity water waves on a plane beach. The data include incident and outgoing wave amplitudes, together with shoreline oscillation amplitudes at long-wave frequencies, from which the correlation between forced long waves and short-wave groups is examined. A detailed analysis of the cross-shore structure of the long-wave motion is presented, and the observations are critically compared with existing theories for two-dimensional surf-beat generation. The surf beat shows a strong dependency on normalized surf-zone width, consistent with long-wave forcing by a time-varying breakpoint, with little evidence of the release and reflection of incident bound long waves for the random-wave simulations considered. The seaward-propagating long waves show a positive correlation with incident short-wave groups and are linearly dependent on short-wave amplitude. The phase relationship between the incident bound long waves and radiated free long waves is also consistent with breakpoint forcing. In combination with previous work, the present data suggest that the breakpoint variability may be the dominant forcing mechanism during conditions with steep incident short waves.

Magnetic component of narrowband ion cyclotron waves in the auroral zone

Abstract: [1] We report observations of waves near the local proton cyclotron frequency and its lowest harmonics, made by the Plasma Wave Instrument on board the Polar spacecraft, on orbits for which the perigee (at an altitude of 1 Earth radius) was in or near the southern auroral zone. The electromagnetic nature of these waves was revealed by measuring their magnetic components simultaneously with two independent antenna systems, one a single loop and the other a set of triaxial search coils. Waves of this kind were found in the southern auroral zone on about a third of the orbits examined. Peaks in the magnetic field power spectra occurred at frequencies both below and above the fundamental cyclotron frequency. The ratio of the amplitudes of the electric and magnetic fluctuations was usually greater than the speed of light, suggesting that we observe a magnetic component related to the wave mode customarily called electrostatic ion cyclotron waves. The fluctuating vector of the wave magnetic field was in or close to the plane perpendicular to the static magnetic field. Our main result is that its polarization, which covered a broad range from left-hand elliptic to right-hand elliptic, can be explained by the superposition of many linearly polarized waves.

Observation of depression solitary surface waves on a thin fluid layer.

Abstract: We report the observation of depression solitary surface waves on a layer of mercury when its depth is thin enough compared to the capillary length. These waves, as well as the well known elevation solitary waves, are studied with a new measurement technique using inductive sensors. The shape of the solitary waves, their amplitude-dependent velocity, and their damping rates by viscosity are found in good agreement with theoretical predictions.

Stable scattering-matrix method for surface acoustic waves in piezoelectric multilayers

Abstract: A scattering matrix approach is proposed to avoid numerical instabilities arising with the classical transfer matrix method when analyzing the propagation of plane surface acoustic waves in piezoelectric multilayers. The method is stable whatever the thickness of the layers, and the frequency or the slowness of the waves. The computation of the Green’s function and of the effective permittivity of the multilayer is outlined. In addition, the method can be easily extended to the case of interface acoustic waves.

Ultrasonic guided waves for steel bar concrete interface testing

Abstract: The feasibility of detecting and quantifying delamination at the interface between steel bar and concrete using ultrasonic guided waves is investigated in this paper. These waves can propagate a long distance along the reinforcing steel bar or concrete beam as guided waves and are sensitive to the interface bonding condition between the steel bar and concrete. The traditional ultrasonic methods are good for detecting large voids in concrete but not very efficient for detecting delamination at the interface between concrete and steel bar since they use reflection, transmission and scattering of longitudinal waves by internal discontinuities. In this study, special solid couplers between the steel bar (or concrete beam) and ultrasonic transducers have been used to launch flexural cylindrical guided waves (or lamb waves) in the steel bar (or concrete). This investigation shows that the guided wave testing technique is an efficient and effective tool for health monitoring of reinforced concrete structures.

Eigenmodes for capillary tubes with dielectric walls and ultraintense laser pulse guiding.

Abstract: The properties of the eigenmodes of a capillary tube are examined in the context of ultrashort intense laser pulse guiding. The dispersion relation for the eigenmodes of a cylindrical hollow waveguide is derived and the family of eigenmodes EH(nus) is shown to be a solution of the wave equation up to the first order under the condition k(0)a >>1, where k(0) is the light wave number and a the capillary tube radius. The expressions of the fields for the eigenmodes are given at zero and first order of a small parameter equal to the ratio of the perpendicular to longitudinal wave number and the absorbed intensity at the wall is estimated.

Experiments on ion-acoustic shock waves in a dusty plasma

Abstract: Dust ion-acoustic shock waves have been investigated experimentally in a homogeneous unmagnetized dusty double-plasma device. An initial compressional wave with a ramp shape steepens to form oscillations at the leading part due to dispersion. The oscillation develops to a train of solitons when the plasma contains no dust grain. The wave becomes an oscillatory shock wave when the dust is mixed in the plasma and the density of the dust grains is smaller than a critical value. When the dust density is larger than the critical value, only steepening is observed at the leading part of the wave and a monotonic shock structure is observed. The velocity and width of the shock waves are measured and compared with results of numerical integrations of the modified Korteweg–de Vries–Burgers equation.

The excitation, propagation and dissipation of waves in accretion discs: the non-linear axisymmetric case

Abstract: We analyse the non-linear propagation and dissipation of axisymmetric waves in accretion discs using the ZEUS-2D hydrodynamics code. The waves are numerically resolved in the vertical and radial directions. Both vertically isothermal and thermally stratified accretion discs are considered. The waves are generated by means of resonant forcing, and several forms of forcing are considered. Compressional motions are taken to be locally adiabatic (γ = 5/3). Prior to non-linear dissipation, the numerical results are in excellent agreement with the linear theory of wave channelling in predicting the types of modes that are excited, the energy flux by carried by each mode, and the vertical wave energy distribution as a function of radius. In all cases, waves are excited that propagate on both sides of the resonance (inwards and outwards). For vertically isothermal discs, non-linear dissipation occurs primarily through shocks that result from the classical steepening of acoustic waves. For discs that are substantially thermally stratified, wave channelling is the primary mechanism for shock generation. Wave channelling boosts the Mach number of the wave by vertically confining the wave to a small cool region at the base of the disc atmosphere. In general, outwardly propagating waves with Mach numbers near resonance M r ≥ 0.01 undergo shocks within a distance of order the resonance radius.

Non-existence of solitary water waves in three dimensions.

Abstract: In the subject of free–surface water waves, solitary waves play an important role in the theory of two–dimensional fluid motions. These are steady solutions to the Euler equations that are localized, positively elevated above the mean fluid level and travelling at velocities with supercritical Froude number. They provide a stable mechanism in bodies of water for transport of mass, momentum and energy over long distances. In this paper, we prove that in the three– (or higher–) dimensional problem of surface water waves, there do not exist any localized steady positive solutions to the Euler equations.

Transverse dynamics of dispersive Alfvén waves. I. Direct numerical evidence of filamentation

Abstract: The three-dimensional dynamics of a small-amplitude monochromatic Alfven wave propagating along an ambient magnetic field is simulated by direct numerical integration of the Hall-magnetohydrodynamics equations. As predicted by the two-dimensional nonlinear Schrodinger equation or by more general amplitude equations retaining the coupling to low-frequency magnetosonic waves, the transverse instability of the pump leads to wave collapse and formation of intense magnetic filaments, in spite of the presence of competing, possibly linearly dominant, instabilities that in some instances distort the above structures. In computational boxes, including a large number of pump wavelengths, an early arrest of the collapse is possible under the effect of quasi-transverse instabilities that drive magnetosonic waves and also prescribe the directions of the filaments.