Showing papers on "Wave propagation published in 1997"

Nonlinear optical pulse propagation in the single-cycle regime

Abstract: A general three-dimensional wave equation first order in the propagation coordinate is derived covering a broad range of phenomena in nonlinear optics. This equation provides an accurate description of the evolution of the wave packet envelope down to pulse durations as short as one carrier oscillation cycle. The concept of envelope equations is found to be applicable to the single-cycle regime of nonlinear optics.

The role of gravity waves in the quasi-biennial oscillation

Abstract: The role of gravity wave momentum transport in the quasi-biennial oscillation (QBO) is investigated using a two-dimensional numerical model. In order to obtain an oscillation with realistic vertical structure and period, vertical momentum transport in addition to that of large-scale, long-period Kelvin and Rossby-gravity waves is necessary. The total wave flux required for the QBO is sensitive to the rate of upwelling, due to the Brewer-Dobson circulation, which can be estimated from the observed ascent of water vapor anomalies in the tropical lower stratosphere. Although mesoscale gravity waves contributeto mean flow acceleration, it is unlikely that the momentum flux in these waves is adequate forthe QBO, especially if their spectrum is shifted toward westerly phase speeds. Short-period Kelvin and inertia-gravity waves at planetary and intermediate scales also transport momentum. Numerical results suggest that the flux in all vertically propagating waves (planetary-scale equatorial modes, intermediate inertia-gravity waves, and mesoscale gravity waves), in combination, is sufficient to obtain a QBO with realistic Brewer-Dobson upwelling if the total wave flux is 2–4 times as large as that of the observed large-scale, long-period Kelvin and Rossby-gravity waves. Lateral propagation of Rossby waves from the winter hemisphere is unnecessary in this case, although it may be important in the upper and lowermost levels of the QBO and subtropics.

Self-focusing and guiding of short laser pulses in ionizing gases and plasmas

Abstract: Several features of intense, short-pulse (/spl lsim/1 ps) laser propagation in gases undergoing ionization and in plasmas are reviewed, discussed, and analyzed. The wave equations for laser pulse propagation in a gas undergoing ionization and in a plasma are derived. The source-dependent expansion method is discussed, which is a general method for solving the paraxial wave equation with nonlinear source terms. In gases, the propagation of high-power (near the critical power) laser pulses is considered including the effects of diffraction, nonlinear self-focusing, ionization, and plasma generation. Self-guided solutions and the stability of these solutions are discussed. In plasmas, optical guiding by relativistic effects, ponderomotive effects, and preformed density channels is considered. The self consistent plasma response is discussed, including plasma wave effects and instabilities such as self-modulation. Recent experiments on the guiding of laser pulses in gases and in plasmas are briefly summarized.

Wave Propagation in Structures: Spectral Analysis Using Fast Discrete Fourier Transforms

Abstract: 1 Spectral Analysis of Wave Motion.- 1.1 Continuous Fourier Transforms.- 1.2 Discrete Fourier Transform.- 1.3 Examples Using the FFT Algorithm.- 1.4 Experimental Aspects of Wave Signals.- 1.5 Spectral Analysis of Wave Motion.- 1.6 Propagating and Reconstructing Waves.- Problems.- 2 Longitudinal Waves in Rods.- 2.1 Elementary Rod Theory.- 2.2 Basic Solution for Waves in Rods.- 2.3 Dissipation in Rods.- 2.4 Coupled Thermoelastic Waves.- 2.5 Reflections and Transmissions.- 2.6 Distributed Loading.- Problems.- 3 Flexural Waves in Beams.- 3.1 Bernoulli-Euler Beam Theory.- 3.2 Basic Solution for Waves in Beams.- 3.3 Bernoulli-Euler Beam with Constraints.- 3.4 Reflection of Flexural Waves.- 3.5 Curved Beams and Rings.- 3.6 Coupled Beam Structure.- Problems.- 4 Higher-Order Waveguides.- 4.1 Waves in Infinite Media.- 4.2 Semi-Infinite Media.- 4.3 Doubly Bounded Media.- 4.4 Doubly Bounded Media: Lamb Waves.- 4.5 Hamilton's Principle.- 4.6 Modified Beam Theories.- 4.7 Modified Rod Theories.- Problems.- 5 The Spectral Element Method.- 5.1 Structures as Connected Waveguides.- 5.2 Spectral Element for Rods.- 5.3 Spectral Element for Beams.- 5.4 General Frame Structures.- 5.5 Structural Applications.- 5.6 Waveguides with Varying Cross Section.- 5.7 Spectral Super-Elements.- 5.8 Impact Force Identification.- Problems.- 6 Waves in Thin Plates.- 6.1 Plate Theory.- 6.2 Point Impact of a Plate.- 6.3 Wavenumber Transform Solution.- 6.4 Waves Reflected from a Straight Edge.- 6.5 Scattering of Flexural Waves.- 6.6 Lateral Boundary Conditions.- 6.7 Curved Plates and Shells.- Problems.- 7 Structure-Fluid Interaction.- 7.1 Acoustic Wave Motion.- 7.2 Plate-Fluid Interaction.- 7.3 Double Panel Systems.- 7.4 Waveguide Modeling.- 7.5 Radiation from Finite Plates.- 7.6 Cylindrical Cavity.- Problems.- 8 Thin-Walled Structures.- 8.1 Membrane Spectral Elements.- 8.2 Spectral Elements for Flexure.- 8.3 Folded Plate Structures.- 8.4 Structural Applications.- 8.5 Segmented Cylindrical Shells.- 8.6 Future of Spectral Elements.- Problems.- Afterword.- Appendix: Bessel Functions.- References.

Kinetic modeling of intense, short laser pulses propagating in tenuous plasmas

Abstract: Fast time averaged equations are derived for the motion of particles and the generation of electromagnetic wake fields under the action of the ponderomotive potential of an ultraintense laser pulse propagating through a tenuous plasma. Based on these averaged equations, a new particle code is designed which calculates the particle trajectories on the plasma period time scale. The regime of total cavitation of the plasma is investigated. It is found that stable propagation over a long distance is possible in this regime, and that energetic electrons are produced with a simple characteristic dependence of their angle of deflection on energy. This new code allows for computationally efficient modeling of pulse propagation over great distances.

Propagation of Sound in a Bose-Einstein Condensate

Abstract: Sound propagation has been studied in a magnetically trapped dilute Bose-Einstein condensate. Localized excitations were induced by suddenly modifying the trapping potential using the optical dipole force of a focused laser beam. The resulting propagation of sound was observed using a novel technique, rapid sequencing of nondestructive phase-contrast images. The speed of sound was determined as a function of density and found to be consistent with Bogoliubov theory. This method may generally be used to observe high-lying modes and perhaps second sound.

Electroseismic waves from point sources in layered media

Abstract: In a porous material saturated by a fluid electrolyte, mechanical and electromagnetic (EM) disturbances are coupled. The coupling is electrokinetic in nature. The seismic waves generate relative fluid-solid motion that induces an electrical streaming current. When a seismic pulse traverses contrasts in elastic and/or fluid-chemistry properties, the streaming-current imbalance creates dipolar and multipolar charge separations across the interface that, in turn, produce EM disturbances that are measurable at the earth's surface. This paper numerically determines a full-waveform electroseismic point-source response in a stratified porous medium. It is shown that the macroscopic governing equations controlling the coupled electromagnetics and acoustics of porous media decouple into two sets corresponding to vertical or horizontal polarization of the transverse wave fields. The frequency content of the converted EM field has the same frequency content (at the generating interface) as the incident seismic pulse. Snapshots in time and converted EM amplitudes versus source to antenna offset are calculated for contrasts in mechanical and/or electrical medium properties. The converted EM radiation pattern away from the interface is similar to having an effective vertical-electric dipole centered right beneath the source on the contrast. The transverse magnetic mode amplitudes fall off rapidly with distance, from the generating interface thus suggesting the importance of a vertical electroseismic profiling geometry to record the converted EM signal at antennas close to an interface of interest.

Breaking criterion and characteristics for solitary waves on slopes

Abstract: ABST.RACT: Sho~ling and breaki,ng of solitary waves is computed on slopes from 1:100 to 1:8 using an expenmentally validated fully nonhnear wave model based on potential flow equations. Characteristics of waves are computed at and beyond the breaking point, and geometric self-similarities of breakers are discussed as a fun?tion of w~ve height and bottom slope. No wave breaks for slopes steeper than 12°. A breaking criterion is denved for rmlde.r slopes, based on val~es of a nondimensional slope parameter So' This criterion predicts both whethe~ waves wIll bre~ or ~ot and which type of breaking will occur (spilling, plunging, or surging). Empirical expressIOns for the bre~ng mdex and for t~e depth and celerity at breaking are derived based on computations. All resul~s agree ~ell With laboratory expenments. The nonlinear shallow water equations fail to predict these results w~th sUfficle~t accuracy at the breaking point. Prebreaking shoaling rates follow a more complex path ~han prevlOus!y reah~ed. Postbreaking beha~iors exhibit a rapid (nondissipative) decay, also observed in exper­ Iments, associated With a transfer of potential energy into kinetic energy. Wave celerity decreases in this zone of rapid decay.

Determination of the dust screening length by laser-excited lattice waves

Abstract: The screening of dust particles immersed in the sheath of a parallel plate rf discharge in helium is studied by excitation of waves in a linear chain arrangement. The waves are excited by the radiation pressure of a modulated laser beam. The measured dispersion relation is compared with a one-dimensional dust lattice wave to obtain the shielding length. Dust acoustic waves are not compatible with the measured dispersion relation. {copyright} {ital 1997} {ital The American Physical Society}

Reflection moveout and parameter estimation for horizontal transverse isotropy

Abstract: Transverse isotropy with a horizontal axis of symmetry (HTI) is the simplest azimuthally anisotropic model used to describe fractured reservoirs that contain parallel vertical cracks. Here, I present an exact equation for normal-moveout (NMO) velocities from horizontal reflectors valid for pure modes in HTI media with any strength of anisotropy. The azimuthally dependent P -wave NMO velocity, which can be obtained from 3-D surveys, is controlled by the principal direction of the anisotropy (crack orientation), the P -wave vertical velocity, and an effective anisotropic parameter equivalent to Thomsen9s coefficient δ. An important parameter of fracture systems that can be constrained by seismic data is the crack density, which is usually estimated through the shear-wave splitting coefficient γ. The formalism developed here makes it possible to obtain the shear-wave splitting parameter using the NMO velocities of P and shear waves from horizontal reflectors. Furthermore, γ can be estimated just from the P -wave NMO velocity in the special case of the vanishing parameter e, corresponding to thin cracks and negligible equant porosity. Also, P -wave moveout alone is sufficient to constrain γ if either dipping events are available or the velocity in the symmetry direction is known. Determination of the splitting parameter from P -wave data requires, however, an estimate of the ratio of the P -to- S vertical velocities (either of the split shear waves can be used). Velocities and polarizations in the vertical symmetry plane of HTI media, that contains the symmetry axis, are described by the known equations for vertical transverse isotropy (VTI). Time-related 2-D P -wave processing (NMO, DMO, time migration) in this plane is governed by the same two parameters (the NMO velocity from a horizontal reflector and coefficient η) as in media with a vertical symmetry axis. The analogy between vertical and horizontal transverse isotropy makes it possible to introduce Thomsen parameters of the “equivalent” VTI model, which not only control the azimuthally dependent NMO velocity, but also can be used to reconstruct phase velocity and carry out seismic processing in off-symmetry planes.

Thin electromagnetic wave absorber for quasi-microwave band containing aligned thin magnetic metal particles

Abstract: Soft magnetic material has been produced in which flaky thin amorphous metal particles, about 2 /spl mu/m thick, are aligned in polymer in the direction perpendicular to electromagnetic wave propagation. This material yields a permeability two to three times higher than the spinel-type ferrite system in the quasi-microwave band. We have designed a thin wave absorber composed of the present material by introducing a low-permittivity area such as a free space into the present metal-containing material. This decreases the average permittivity, striking a balance between complex permeability and permittivity values, and thus reducing the reflection coefficient of the absorber. A thin (about 3-mm thick) wave absorber with a reflection loss of over 30 dB in the quasi-microwave band was successfully obtained when the free space region was 5% of the total volume.

On Wave Propagation in Elastic Solids with Cracks

Abstract: Boundary Integral Methods Elastodynamic Stress Intensity Factors Time-harmonic Wave Propagation Anti-plane Interface Cracks Wave Attenuation and Dispersion Damage Mechanics Dynamic Fracture Mechanics Mechanics of Materials Ultrasonic Quantative Non-destructive Testing.

Development of a Third Generation Shallow-Water Wave Model with Unstructured Spatial Meshing

Abstract: A numerical third-generation wave model dedicated both to deep water and nearshore applications is presented and applied to several test-cases to highlight its capabilities. Among its main features, this model uses a finite-elements technique for the discretization of the modelled area, which makes it suitable to represent complex bottom topographies and irregular shorelines. Furthermore, the piece-wise ray method used for wave propagation allows to use rather large time-steps, which in turn allows to keep the computational time at a very moderate level. The implementation of shallow-water physics in the model is also described, in particular with respect to depth-induced breaking. Several applications of the model are presented and compared to field or laboratory data for their validation. Finally, the main research and development items are mentioned and discussed.

Hybrid modeling of P-SV seismic motion at inhomogeneous viscoelastic topographic structures

Abstract: A new hybrid two-step method for computation of P-SV seismic motion at inhomogeneous viscoelastic topographic structure is presented. The method is based on a combination of the discrete-wavenumber (DW), finite-difference (FD), and finite-element (FE) methods. In the first step, the DW method is used to calculate the source radiation and wave propagation in the background 1D medium. In the second step, the FD-FE algorithm is used to compute the wave propagation along the topographic structure. The accuracy of the method has been separately tested for inclusion of the attenuation and for inclusion of the free-surface topography through numerical comparisons with analytical and independent numerical methods. The method is a generalization of the hybrid DW-FD method of Zahradnik and Moczo (1996) for localized structures with a flat free surface. Numerical computations for a ridge, sediment valley, and the ridge neighboring the sediment valley show that a ridge can considerably influence the response of the neighboring sediment valley. This means that the neighboring topographic feature should be taken into account even when we are only interested in the valley response.

Propagation of near-inertial oscillations through a geostrophic flow

Abstract: The method of multiple time scales is used to obtain an approximate description of the linear propagation of near-inertial oscillations (NIOs) through a three-dimensional geostrophic flow. This 'NIO equation' uses a complex field, M(x, y, z, t), related to the demodulated horizontal velocity by M z = exp (if 0 t)(u + iv), where f 0 is the inertial frequency. The three processes of wave dispersion, advection by geostrophic velocity and refraction (geostrophic vorticity slightly shifts the local inertial frequency) are all included in the formulation. The NIO equation has an energy conservation law, so that there is no transfer of energy between NIOs and the geostrophic flow in the approximation scheme. As an application, the NIO equation is used to examine propagation of waves through a field of smaller scale, geostrophic eddies. The spatially local ζ/2 frequency shift, identified by earlier WKB calculations (ζ is the vertical vorticity of the geostrophic eddies), is not expressed directly in the wave field: the large-scale NIO samples regions of both positive and negative ζ so that there is cancellation. Instead, the ζ/2 frequency shift is rectified to produce an average dispersive effect. The calculation predicts that an NIO with infinite horizontal scale has a frequency shift -Kf 0 m 2 /N 2 where K is average kinetic energy density of the geostrophic eddies, m the vertical wavenumber of the NIO, f 0 the inertial frequency and N the buoyancy frequency. Because of the dependence of the frequency shift on m 2 , there is an effective vertical dispersion, whose strength is proportional to the eddy kinetic energy. This process greatly increases the vertical propagation rate of synoptic scale NIOs.

Kinetic Alfvén waves and plasma transport at the magnetopause

Abstract: Large amplitude compressional type ULF waves can propagate from the magnetosheath to the magnetopause where there are large gradients in density, pressure and magnetic field. These gradients efficiently couple compressional waves with shear/kinetic Alfven waves near the Alfven field-line resonance location (ω=k∥υA). We present a solution of the kinetic-MHD wave equations for this process using a realistic equilibrium profile including full ion Larmor radius effects and wave-particle resonance interactions for electrons and ions to model the dissipation. For northward IMF a KAW propagates backward to the magnetosheath. For southward IMF the wave remains in the magnetopause but can propagate through the k∥=0 location. The quasilinear theory predicts that transport due to KAWs at the magnetopause primarily results from the perpendicular electric field coupling with magnetic drift effects with diffusion coefficient D⟂ ∼ 109 m²/s. For southward IMF additional transport can occur because magnetic islands form at the k∥=0 location. Due to the broadband nature of the observed waves these islands can overlap leading to stochastic transport which is larger than that due to quasilinear effects.

A general method for FDTD modeling of wave propagation in arbitrary frequency-dispersive media

Abstract: A general formulation is presented for finite-difference time-domain (FDTD) modeling of wave propagation in arbitrary frequency-dispersive media. Two algorithmic approaches are outlined for incorporating dispersion into the FDTD time-stepping equations. The first employs a frequency-dependent complex permittivity (denoted Form-1), and the second employs a frequency-dependent complex conductivity (denoted Form-2). A Pade representation is used in Z-transform space to represent the frequency-dependent permittivity (Form-1) or conductivity (Form-2). This is a generalization over several previous methods employing either Debye, Lorentz, or Drude models. The coefficients of the Pade model may be obtained through an optimization process, leading directly to a finite-difference representation of the dispersion relation, without introducing discretization error. Stability criteria for the dispersive FDTD algorithms are given. We show that several previously developed dispersive FDTD algorithms can be cast as special cases of our more general framework. Simulation results are presented for a one-dimensional (1-D) air/muscle example considered previously in the literature and a three-dimensional (3-D) radiation problem in dispersive, lossy soil using measured soil data.

Elastic wave band gaps and defect states in two-dimensional composites

Abstract: Using the plane-wave expansion method, we study the propagation of elastic waves through two-dimensional (2-D) periodic composites which exhibit full band gaps for all the polarizations and directions of the displacements. Defect states created inside those band gaps are also studied by disturbing the periodicity of the lattice. Systems exhibiting such kinds of states can be used as acoustical filters.

Estimates of momentum flux associated with equatorial Kelvin and gravity waves

Abstract: A new indirect method is proposed to estimate momentum flux based on the theory of slowly varying gravity waves and equatorial waves in vertical shear by Dunkerton [this issue] which explains the discovery by Sato et al. [1994] that the cospectra of temperature and zonal wind fluctuations at Singapore (1.4°N, 104.0°E) are synchronized with the quasi-biennial oscillation (QBO) of mean zonal wind in the stratosphere. The indirect estimates obtained from cospectra correspond to the summation of absolute values of momentum flux associated with each wave, whereas direct estimates from quadrature spectra give the summation of momentum flux. An analysis was made for twice daily rawinsonde data at Singapore. The direct estimate for Kelvin waves (5–20 day components) is 2–9×10−3 m s−2 and accords with the indirect estimate to within the estimation error. This result supports the validity of the indirect method. Although the indirect estimate depends on an assumed wave structure, large values of momentum flux are obtained for all possible equatorial modes having short periods (1–3 days). The indirect estimate for westerly shear is 20–60×10−3 m2 s−2 based on the theory of two-dimensional gravity waves, while the direct estimate is only 0–4×10−3 m2 s−2. The reduction of indirect estimate under the assumption of equatorial waves is about 30–70%. The discrepancy between direct and indirect estimates indicates a large cancelation of positive and negative momentum fluxes. This is the case also for easterly shear. The indirect estimate for westerly shear is almost twice as large as that for easterly shear. The characteristics of waves near the source in the troposphere are thought to be independent of the QBO in the stratosphere, so that the difference in wave activity should be attributed to the differing characteristics of wave propagation under the strong QBO shear. Several possible explanations are discussed. Parameters such as phase velocity and zonal wavelength are estimated from the ratio of potential to kinetic energies assuming that the 1–3 day components are due to equatorial waves. The estimates in this paper were made assuming that the observed frequencies are actual ground-based wave frequencies. If there is aliasing from higher frequencies than 1 day, the actual momentum fluxes can be significantly larger than the estimated values.

Stationary rossby‐wave propagation in a baroclinic atmosphere

Abstract: Observational studies of teleconnections in both soisticial seasons have suggested various patterns of behaviour linked mainly to westerly jets and equatorial westerlies. These have been interpreted using barotropic Rossby-wave theory, and simulated using stationary forcing in barotropic models linearized about 300 hPa flows. In this paper the relevant propagation behaviour is investigated using a baroclinic model with three-dimensional, climatological basic states. Time integrations are performed using localized thermal forcing as a wavemaker. The propagation results are qualitatively very similar to those obtained with the barotropic model, though there are quantitative differences. The westerly jets still act as strong waveguides. The shorter wavelengths and smaller wave-activity speeds found with the baroclinic model are generally in better agreement with observation. Propagation into and from the upper tropospheric equatorial westerlies in the east Pacific, propagation across North America and propagation from Europe across the Arabian Gulf are all found. The extent to which upper tropospheric westerlies reach towards the equator influences the propagation into those regions. Barotropic models can only represent such behaviour if the basic state reflects the near-equatorial upper tropospheric zonal wind structure.

Simulation of ultrasonic pulse propagation through the abdominal wall

Abstract: Ultrasonic pulse propagation through the human abdominal wall has been simulated using a model for two-dimensional propagation through anatomically realistic tissue cross sections. The time-domain equations for wave propagation in a medium of variable sound speed and density were discretized to obtain a set of coupled finite-difference equations. These difference equations were solved numerically using a two-step MacCormack scheme that is fourth-order accurate in space and second-order accurate in time. The inhomogeneous tissue of the abdominal wall was represented by two-dimensional matrices of sound speed and density values. These values were determined by processing scanned images of abdominal wall cross sections stained to identify connective tissue, muscle, and fat, each of which was assumed to have a constant sound speed and density. The computational configuration was chosen to simulate that of wavefront distortion measurements performed on the same specimens. Qualitative agreement was found betwee...

A Model Study of Zonal Forcing in the Equatorial Stratosphere by Convectively Induced Gravity Waves

Abstract: A two-dimensional cloud-resolving model is used to examine the possible role of gravity waves generated by a simulated tropical squall line in forcing the quasi-biennial oscillation (QBO) of the zonal winds in the equatorial stratosphere. A simulation with constant background stratospheric winds is compared to simulations with background winds characteristic of the westerly and easterly QBO phases, respectively. In all three cases a broad spectrum of both eastward and westward propagating gravity waves is excited. In the constant background wind case the vertical momentum flux is nearly constant with height in the stratosphere, after correction for waves leaving the model domain. In the easterly and westerly shear cases, however, westward and eastward propagating waves, respectively, are strongly damped as they approach their critical levels, owing to the strongly scale-dependent vertical diffusion in the model. The profiles of zonal forcing induced by this wave damping are similar to profiles given by critical level absorption, but displaced slightly downward. The magnitude of the zonal forcing is of order 5 m s21 day21. It is estimated that if 2% of the area of the Tropics were occupied by storms of similar magnitude, mesoscale gravity waves could provide nearly 1/4 of the zonal forcing required for the QBO.

On the quasi-analytic treatment of hysteretic nonlinear response in elastic wave propagation

Abstract: Microscopic features and their hysteretic behavior can be used to predict the macroscopic response of materials in dynamic experiments. Preisach modeling of hysteresis provides a refined procedure to obtain the stress–strain relation under arbitrary conditions, depending on the pressure history of the material. For hysteretic materials, the modulus is discontinuous at each stress–strain reversal which leads to difficulties in obtaining an analytic solution to the wave equation. Numerical implementation of the integral Preisach formulation is complicated as well. Under certain conditions an analytic expression of the modulus can be deduced from the Preisach model and an elementary description of elastic wave propagation in the presence of hysteresis can be obtained. This approach results in a second-order partial differential equation with discontinuous coefficients. Classical nonlinear representations used in acoustics can be found as limiting cases. The differential equation is solved in the frequency do...

Numerical Generation and Absorption of Fully Nonlinear Periodic Waves

Abstract: Permanent form periodic waves with zero-average mass flux are generated in a two-dimensional numerical wave tank solving fully nonlinear potential flow equations. An absorbing beach is modeled at the end of the tank in which (1) an external free-surface pressure absorbs energy from high frequency waves; and (2) a pistonlike condition absorbs energy from low-frequency waves. A feedback mechanism adaptively calibrates the beach parameters to absorb the period-averaged energy of incident waves. Wave generation and absorption are validated over constant depth, for tanks and beaches of various lengths, and optimal parameter values are identified for which reflection from the beach is reduced to a few percent. Shoaling of periodic waves is then modeled over a 1:50 slope, up to very close to the breaking point. A quasi-steady state is reached in the tank for which (not previously calculated) characteristics of fully nonlinear shoaling waves are obtained.

Generalized theory of helicon waves. I. Normal modes

Abstract: The theory of helicon waves is extended to include finite electron mass. This introduces an additional branch to the dispersion relation that is essentially an electron cyclotron or Trivelpiece–Gould (TG) wave with a short radial wavelength. The effect of the TG wave is expected to be important only for low dc magnetic fields and long parallel wavelengths. The normal modes at low fields are mixtures of the TG wave and the usual helicon wave and depend on the nature of the boundaries. Computations show, however, that since the TG waves are damped near the surface of the plasma, the helicon wave at high fields is almost exactly the same as is found when the electron mass is neglected.

Alfven Wave Phase Mixing as a Source of Fast Magnetosonic Waves

Abstract: The nonlinear excitation of fast magnetosonic waves by phase mixing Alfven waves in a cold plasma with a smooth inhomogeneity of density across a uniform magnetic field is considered If initially fast waves are absent from the system, then nonlinearity leads to their excitation by transversal gradients in the Alfven wave The efficiency of the nonlinear Alfven–fast magnetosonic wave coupling is strongly increased by the inhomogeneity of the medium The fast waves, permanently generated by Alfven wave phase mixing, are refracted from the region with transversal gradients of the Alfven speed This nonlinear process suggests a mechanism of indirect plasma heating by phase mixing through the excitation of obliquely propagating fast waves

Numerical simulation of the evolution of Tollmien–Schlichting waves over finite compliant panels

Abstract: The evolution of two-dimensional Tollmien–Schlichting waves propagating along a wall shear layer as it passes over a compliant panel of finite length is investigated by means of numerical simulation. It is shown that the interaction of such waves with the edges of the panel can lead to complex patterns of behaviour. The behaviour of the Tollmien–Schlichting waves in this situation, particularly the effect on their growth rate, is pertinent to the practical application of compliant walls for the delay of laminar–turbulent transition. If compliant panels could be made sufficiently short whilst retaining the capability to stabilize Tollmien–Schlichting waves, there is a good prospect that multiple-panel compliant walls could be used to maintain laminar flow at indefinitely high Reynolds numbers.We consider a model problem whereby a section of a plane channel is replaced with a compliant panel. A growing Tollmien–Schlichting wave is then introduced into the plane, rigid-walled, channel flow upstream of the compliant panel. The results obtained are very encouraging from the viewpoint of laminar-flow control. They indicate that compliant panels as short as a single Tollmien–Schlichting wavelength can have a strong stabilizing effect. In some cases the passage of the Tollmien–Schlichting wave over the panel edges leads to the excitation of stable flow-induced surface waves. The presence of these additional waves does not appear to be associated with any adverse effect on the stability of the Tollmien–Schlichting waves. Except very near the panel edges the panel response and flow perturbation can be represented by a superposition of the Tollmien–Schlichting wave and two other eigenmodes of the coupled Orr–Sommerfeld/compliant-wall eigensystem.The numerical scheme employed for the simulations is derived from a novel vorticity–velocity formulation of the linearized Navier–Stokes equations and uses a mixed finite-difference/spectral spatial discretization. This approach facilitated the development of a highly efficient solution procedure. Problems with numerical stability were overcome by combining the inertias of the compliant wall and fluid when imposing the boundary conditions. This allowed the interactively coupled fluid and wall motions to be computed without any prior restriction on the form taken by the disturbances.

Formulation and validation of Berenger's PML absorbing boundary for the FDTD simulation of acoustic scattering

Abstract: Berenger's perfectly matched layer (PML) absorbing boundary condition for electromagnetic (EM) waves is derived to absorb 2-D and 3-D acoustic waves in finite difference time domain (FDTD) simulation of acoustic wave propagation and scattering. A PML medium suitable for acoustic waves is constructed. Plane wave propagation in the PML medium is solved for both 2-D and 3-D cases and explicit FDTD boundary conditions are derived. The equations show that a matched PML medium is a perfect simulation of free space in that a plane wave does not change its direction of propagation or its speed when it propagates from free space into a matched PML medium. FDTD simulation of a pulsed point source propagating in two dimensions is carried out to test the performance of the PML boundary for acoustic waves. Results show that an eight layer PML boundary condition reduces the reflected error 40 dB over Mur's second order boundary condition.

A climatology of F region gravity wave propagation over the middle and upper atmosphere radar

Abstract: By observing the ionospheric F region simultaneously in multiple beams with the middle and upper atmosphere radar, we have been able to track the passage of gravity waves and measure their propagation characteristics. Here we develop a climatology of wave propagation based on the observation of 58 daytime experiments conducted during 1986–1994. The thermosphere seems to be continuously swept by waves detectable by an incoherent scatter radar. These waves generally come for hours on end from a consistent or slowly varying direction, which can be any direction on a given day. Statistically, the waves show a moderate preference for southward travel, with this preference being reduced or shifted to southeastward travel during disturbed times. On average, the horizontal phase trace speed remains near 240 m/s for all periods inspected (40–130 min). This speed matches the behavior expected for lossless waves with 150–200 km vertical wavelength. We find small variability in this relation for different times of day, seasons, solar and magnetic conditions, and directions of wave travel, though waves on disturbed days seem to travel moderately faster on solar minimum mornings.