Showing papers on "Longitudinal wave published in 1974"

Acoustic‐gravity waves in the upper atmosphere

Abstract: In this paper we review the theory of acoustic-gravity waves, the interaction of such waves with the ionosphere, the experimental support for the existence of such waves in the upper atmosphere, and the role played by acoustic-gravity waves in thermospheric dynamics. After a thorough discussion on the properties of acoustic-gravity waves in an ideal isothermal atmosphere, the effects produced by horizontal winds, sharp boundary discontinuities, and dissipative processes are discussed. The generation of these waves by stationary or moving sources is then treated. It is shown that the atmospheric response to a stationary impulse source can be described by the emission of three waves: acoustic, buoyancy, and gravity. These discussions are then followed by reviewing propagation effects in a realistic atmosphere for both free waves and guided waves. Recent numerical results are given. When acoustic-gravity waves propagate through the ionosphere, interaction between the wave and the ionosphere will take place. The physical processes involved in such an interaction are examined.

Thermal Self-Focusing of Electromagnetic Waves in Plasmas

Abstract: An intense electromagnetic wave propagating in a collisional plasma is found to be unstable to a thermal self-focusing instability by a self-consistent solution of the hydrodynamic, heat conductivity, and wave propagation equations. The results are applied to ionospheric modifications and proposed power transmission experiments, and to laser-plasma interactions.

Experimental study of internal waves over a slope

Abstract: Internal waves of the fundamental mode propagating into a shoaling region have been studied experimentally in a continuously stratified fluid. The waves divide into three classes depending upon the ratio of the bottom slope γ to the wave-characteristic slope c. For γ/c 1, the waves are inhomogeneous and have complex spatial dependence.

Whistler waves observed upstream from collisionless shocks

Abstract: Waves in the frequency range 0.5 - 4 Hz were studied in the region upstream of the earth's bow shock using data from the fluxgate magnetic field experiment on IMP-6. Analysis of 150 examples of these waves during a three month interval indicates that amplitudes are generally less than 1 or 2 gammas and propagation directions generally make angles of between 20 and 40 degrees with the field direction. The waves as measured in the spacecraft frame of reference are either left or right hand polarized with respect to the average field direction. It is concluded that the observed waves are right handed waves in the plasma frame of reference with wavelengths of approximately 100 km propagating upstream in the whistler mode. Doppler shifting reduces the observed frequencies in the spacecraft frame and reverses the observed polarization for those waves propagating more directly upstream. Similar waves are seen ahead of most interplanetary shocks.

Krylov‐Bogoliubov‐Mitropolsky method for nonlinear wave modulation

Abstract: The Krylov‐Bogoliubov‐Mitropolsky perturbation method is applied to systems of nonlinear dispersive waves including plasma waves such as ion‐acoustic, magneto‐acoustic, and electron plasma waves. It is found that long time slow modulation of the complex wave amplitude can be described by the nonlinear Schrodinger equation for a very wide class of nonlinear dispersive waves.

Excitation of edge waves by waves incident on a beach

Abstract: It is shown theoretically that surface waves incident on a beach from deep water can excite edge waves. In particular, a standing wave normally incident on a beach of constant gentle slope is found to transfer energy to edge waves through a weak resonant interaction resulting from an instability of the incident wave with respect to perturbation by edge waves. The analysis is based on the shallow water approximation and ignores the earth's rotation and consequently applies only to relatively low-mode, high-frequency waves. Coupling coefficients, frequencies, and longshore wave numbers of the excited waves are given. In accordance with Hasselmann's (1967) rule, only edge waves with frequencies lower than the frequency of the incident wave are excited by this mechanism. Viscous effects suggest that an edge wave with a frequency one-half that of the incident wave is preferentially excited.

On a variety of wave phenomena in chemical reactions

Abstract: A variety of wave phenomena are analyzed and discussed for systems in which chemical reactions and transport take place. Certain families of wave solutions of reaction‐transport equations arise owing to the weak stability of a reference state to a class of perturbations. We consider both wave induction by heterogeneities and autonomous waves and seek perturbation solutions which provide the dispersion relation and the wave vector dependence of the amplitude for one‐parameter families of waves characterized by the wave vector. For the case of an arbitrary reaction mechanism possessing a homogeneous steady state we derive, by use of bifurcation theory and frequency renormalization, small amplitude autonomous plane waves and standing and rotating waves. We find solutions corresponding to long wavelength waves, static structures, and phenomena existing only at intermediate frequencies and wavelengths. The theory is found to have a nonuniformity in convergence in the core region of pacemaker and spiral‐like so...

Immersion apparatus for ultrasonic measurements in polymers

Abstract: An immersion apparatus for making ultrasonic measurements in polymers was constructed. A unique feature of this apparatus is that the specimen is held vertically, and the transducers are rotated in order to produce shear waves in the specimen. This arrangement allows measurements to be made through the melting point of crystalline polymers. Sound‐speed measurements, accurate to ±2%, were made on 25 polymers at room temperature and on five of these polymers as a function of temperature. On 15 of the polymers, both longitudinal and shear sound speeds were measured. The longitudinal wave speeds ranged from 2820 to 1020 m/sec, while shear wave speeds ranged from 1230 to 650 m/sec. Using these sound speeds and measured densities, the elastic constants of these polymers were calculated. For four polymers elastic constants as a function of temperature were calculated.

Elastic waves in a fiber-reinforced composite

Abstract: T he propagation of time-harmonic elastic waves in a fiber-reinforced composite is studied. The circular fibers are assumed to be parallel to each other and randomly distributed with a statistically uniform distribution. The direction of propagation and the associated particle motion are considered to be normal to the fibers. It is shown that the average waves in the composite separate into compressional and shear types. General formulae for the complex wave number giving the phase velocity and the damping are obtained. It is shown that these formulae lead to the Hashin-Rosen expressions for the transverse bulk modulus and the lower bound for the transverse rigidity, if the correlation in the positions of the fibers can be ignored. The correlation terms, for exponential correlation, are shown to have a significant effect on the damping property of the composite, especially at high frequencies and concentrations.

A finite amplitude wave on a linear shear current

Abstract: A numerical perturbation procedure is presented that generates water waves propagating over a vertically varying linear shear current. The water surface profile of these waves may be symmetric about the crest, with given height and period, or they may have an irregular water surface profile that has been measured in water of known depth. For waves of the same height the effect of the current is to cause a change in wavelength and hence the kinematics under the wave. Further, the shape of the wave profile is changed significantly.

Compressional waves in fluid‐saturated elastic porous media

Abstract: This article discusses the propagation of compressional waves in fluid‐saturated elastic porous media. Both harmonic and transient pulses are considered. In general, two modes of wave propagation exist. In the case of a transient pulse, these modes lead to a two‐wave structure. It is not possible to obtain closed‐form solutions for the general case of transient loading, but considerable insight may be obtained from certain limiting cases (e.g., no viscous coupling, large viscous coupling) for which analytical solutions are derived by means of Laplace transform techniques. Strong viscous coupling leads to the coalescence of the two wave fronts into a single front; in this case the material behaves like a single continuum with internal dissipation. Solutions for the general case are obtained both by numerical inversion of the Laplace transforms and by direct finite‐difference methods.

Interacting electromagnetic shock waves in general relativity

Abstract: It is shown that the continuity conditions of Lichnerowicz must generally be relaxed in favour of the O'Brien-Synge conditions in the case of shock electromagnetic waves. This is in particular true when two electromagnetic shock waves are in collision. Gravitational impulse waves are produced as a result of the weakened conditions. An exact solution exhibiting this behaviour is derived, and the effect of the impulse waves on a measuring device are compared with experimental results of Weber.

A Modified Korteweg de Vries Equation for Ion Acoustic Waves

Abstract: Three wave mode coupling effects on ion acoustic waves are examined by applying the Fourier transformation method of separation of the nonlinear slow processes for a two component plasma described by the Vlasov equation. Contribution of the three mode coupling terms gives rise to a modified Korteweg de Vries equation with a nonlinear term of the form of { B φ+( C /2)φ 2 }φ x , where B and C are constants determined by the unperturbed state of plasmas. It is found that velocity of a stationary solitary wave depends sensitively on the electronion temperature ratio, and that the equation obtained here enables us to account for the amplitude dependence of the solitary wave velocity observed by Ikezi, Baker and Taylor.

Thermoelastic waves in anisotropic solids

Abstract: As motivated by the recent discovery of heat pulses propagating in dielectric crystals at low temperature, a continuum theory of thermoelasticity, which is modified to include the effect of thermal phonon relaxation, is applied to investigate the propagation of plane harmonic waves in unbounded anisotropic solids Four characteristic wave speeds are found, three being analogous to those of isothermal or adiabatic elastic waves The fourth wave, which is predominantly a temperature disturbance, corresponds to the heat pulses known also as the second sound Velocity, slowness, and wave surfaces of the thermoelastic waves are analyzed and are illustrated with numerical and graphical results for NaF and solid helium crystals A new definition of the group velocity for waves in a dissipative and dispersive anisotropic medium is proposed and is calculated and compared with the energy transport speed of thermoelastic waves

Conversion of Electromagnetic Waves to Electrostatic Waves in Inhomogeneous Plasmas

Abstract: Propagation of electromagnetic waves in a large plasma reveals that refraction effects are much more significant than the amplitude swelling commonly predicted from the reduction in group velocity. Near electromagnetic wave cutoff, direct conversion into short-wavelength electron plasma waves is observed. Strong resonant enhancement of the electric field parallel to the density gradient is measured.

On the backscatter instability of solar wind Alfvén waves

Abstract: A coherent Alfv6n wave propagating along the equilibrium magnetic field is unstable against decay into an Alfv6n wave traveling in the opposite direction and a sound wave (Sagdeer and Galeev, 1969). The stability of incoherent Alfv6n waves against this mode decay is considered, assuming that the sound waves are damped. The criterion for stabilizing waves with power spectral density In ok -N is N > 1. The results indicate that solar wind Alfv6n waves are stable in the wavelength range considered in Mariner 5 ob- servations, although a mild instability is predicted for longer wavelengths. According to the interpretation of Mariner 5 data by Belcher and Davis (1971) the high-velocity solar wind streams and their trailing edges are often characterized at 1 A U by large-amplitude hydromagnetic fluctuations that are almost purely Alfv6nic and almost completely outward propagating with respect to the wind. The term Alfv6nic is used here to de- scribe fluctuations in which the magnitude of the magnetic field is strictly constant, such as circularly polarized waves propagating along the unperturbed field direction. Among the processes that have been proposed for damping of hydromagnetic waves in the solar wind are linear collision- less damping (Barnes, 1966), nonlinear Landau damping (Hollweg, 1971; Lee and Volk, 1973), and steepening followed by dissipation in shocks (Cohen and Kulsrud, 1974). These mechanisms are inoperative for the Alfv6n mode; hence under their influence a random mixture of hydromagnetic waves damps into Alfv6nic fluctuations, such as those observed at 1 A U. On the other hand, the decay instability of Galeev and Oraevskii (1963) results from a mode coupling that is basically insensitive to polarization, and hence in particular can lead to decay of purely Alfv6nic fluctuations. We consider here the stability of solar wind Alfv6n waves against this decay mode. Galeev and Oraevskii noted that an Alfv6n wave is unstable against decay into another Alfv6n wave and a magneto- acoustic wave. For the simple case of propagation along the magnetic field (Sagdeer and Galeev, 1969) the magneto- acoustic wave is a sound wave and the scattered Alfv6n wave travels in the opposite direction from the parent wave. Sagdeev and Galeev consider a monochromatic circularly polarized parent wave; they introduce the decay products as small per- turbations and calculate the growth rate 'c, assuming no linear damping and small/5 -- (Cs/VA) 2, where Cs is the sound speed and vA is the Alfv6n speed. Their result may be written in the form

Thunderstorm-Generated Gravity Waves

Abstract: Internal gravity waves have been recorded at London, Ontario, using a network of three microbarographs. It has been shown from experimental observations that internal gravity waves are generated by thunderstorms. The spectral behavior of these waves has been found to be essentially monochromatic. A simple model for the generation of these waves is presented and it is shown that the observed properties of the waves are in good agreement with the features of the suggested model.

Excess heating of corona and chromosphere above magnetic regions by non- linear Alfven waves

Abstract: Excess heating of the active solar atmosphere is interpreted as the decay of MHD slow-mode waves produced in the corona through the non-linear coupling of Alfven waves supplied from subphotospheric layers It is stressed that the Alfven-mode waves may be very efficiently generated directly in the convection layer under the photosphere in magnetic regions, and that such magnetic regions, at the same time, provide the ‘transparent windows’ for Alfven waves in regard to the Joule and frictional dissipations in the photospheric and subphotospheric layers Though the Alfven waves suffer considerable reflection in the chromosphere and in the transition layer, a certain fraction is propagated out to the corona A large velocity amplitude, exceeding the local Alfven velocity, is attained during the propagation along the magnetic tubes of force into a region of lower density and weaker magnetic field The otherwise divergence-free velocity field in Alfven waves, in such a case, couples with a compressional component (slow-mode waves) which again is of considerable velocity amplitude relative to the local acoustic velocity when estimated by using the formula for non-linear coupling between MHD wave modes derived by Kaburaki and Uchida (1971) Therefore, the compressional waves thus produced through the non-linear coupling of Alfven waves are eventually thermalized to provide a heat source The introduction of this non-linear coupling process and the subsequent thermalization of the slow-mode waves may provide a means of converting the otherwise dissipation-free Alfven mode energy into heat in the corona The liberated heat will readily be redistributed by conduction along the magnetic lines of force, and thus the loop-like structure of the coronal condensations (or probably also the thread-like feature in the general corona) is explained in a natural fashion Matter density in the arches is expected to be higher than the ambient density because of the higher temperature and, consequently, greater scale height in the arches

Reflection and transmission of inhomogeneous waves with particular application to Rayleigh waves

Abstract: The concept of inhomogeneous waves, which is quite common in the electromagnetic literature but not in the seismic, is reviewed. It is shown that the Rayleigh wave results from the constructive interference of a P inhomogeneous wave with an SV inhomogeneous wave. Of some interest is the fact that while the two inhomogeneous waves have prograde elliptical particle motions, they combine to yield the familiar retrograde motion near the surface. These two inhomogeneous waves are the only “allowed” inhomogeneous waves in a homogeneous elastic half-space. More can occur in a layered half-space but they are always discrete in number. However, “non-allowed” inhomogeneous waves often give a very good representation of the wave motion over a restricted area—a fact which is demonstrated for leaky modes and propagation of a Rayleigh wave on a three-quarter space. With this in mind, a formalism is developed for the transmission and reflection of the two allowed inhomogeneous waves making up the Rayleigh wave into nonallowed inhomogeneous waves. These are nonallowed in the sense that they do not fit the boundary conditions at a discrete number of points. Here the ray picture breaks down and diffractive effects occur. Our assumption is that for many interesting cases, these diffractive effects are small and can be ignored. The components of the resultant displacements and stresses from the nonallowed inhomogeneous waves on Rayleigh waves can be obtained by use of a relation due to Herrera, thus yielding the reflection and transmission coefficients. The agreement with previously published values is good. While only normal incidence is considered in this paper, the extension to non-normal incidence is straightforward. The required calculations are well within the capabilities of a small computer such as an IBM 1130.

Application of Linear Inversion Theory Toward the Estimation of Seismic Source Parameters

Abstract: A discussion is given concerning the development of methods for obtaining an accurate representation of the forward elastostatic problem of describing the processes which accompany faulting. A method is suggested by which a more complicated and arbitrary static dislocation function could be approximated with the formulations derived for simple dislocation sources. A stochastic inverse is used to provide optimum estimates of the source description when observed elastostatic phenomena are systematically related to the media response of the various source parameters. This method is applied to the observed static displacement data from the 1964 Alaska earthquake and the 1971 San Fernando, California, earthquake. For the Alaskan event, the surface static displacements are calculated with the finite-element numerical modeling technique in which the effects of known geologic heterogeneities of the region are taken into account. The fault model used is that of a shallow angle fault underthrusting the Alaskan continental block. The calculated optimum static offset, stress drop, and strain energy density along the fault were found to be variable with a maximum offset of about 30 m. The region of maximum stress drop (218 bars) and maximum strain energy density change is found to correspond to the region of maximum compressional wave radiation. The resolution and resolvability of the calculated static fault model is discussed. For the San Fernando earthquake, the static dislocation along the assumed fault plane was also found to vary considerably. The observed surface displacements are fit to a high degree of accuracy by the given model. Included in the inversion data set are changes in the local gravity field caused by the earthquake. These changes can be predicted from known changes in elevation when a Bouguer correction is applied to the gravity data. The spatial and frequency distribution of path-corrected Rayleigh waves from the San Fernando earthquake are systematically related to the faulting process. The surface wave source is taken to be a depth-distributed set of double couples. A least-squares inversion is used to find the set of source parameters which optimally fit the variance-weighted data. The inversion results indicate a depth-distributed moment of 1.7 x 1026 dyne-cm. The slip angles of the sources varied in such a way along the fault that the displacements became more predominantly dip slip as the dislocation propagated upward from the point of initial rupture at about 3.0 km/sec. A sophisticated error analysis is performed to estimate the uncertainties of the calculated model variables. An appendix is included in which the analytical expressions are derived for the complete strain field due to a dislocation on an arbitrarily inclined fault in a homogeneous half-space. Although the expressions are lengthy, the strain values can be calculated quickly on a computer since no numerical integration is necessary.

B. Nonlinear Modulation of Plasma Waves

Abstract: The self-trapping and instabilities of modulated whistler waves propagating along a uniform magnetic field were first studied by Taniuti arid Washimi.l) Using the fluid model for the cold plasma, they derived a dispersive nonlinear equation (the nonlinear Schrodinger equation) to describe a slow modulation of a carrier wave of small but finite amplitude. This equation takes the same form as the equation appearing in the study of self-focusing in nonlinear optics. They then showed that the solitary wave, that is, envelope soliton exists while the plane wave is unstable against a modulation of amplitude and phase. Mizutani and Taniuti2) extended the theory to oblique propagation of stationary waves to obtain the envelope soliton, and later Mizutani3) derived the nonlinear Schrodinger equation for nonstationary oblique propagation and showed the modula~ional instability. These problems were also investigated by Pataraya.4) However, these works are concerned with the propagation of the ·carrier wave at those frequencies for which the group velocity is equal to the phase velocity. The extension to propagation at an arbitrary frequency is straightforward, and this was carried out, using the method of Taniuti and Yajima,5) by Hasegawa6) for the case of propagation along the magnetic field for all the frequencies of whistler waves and also ion-cyclotron waves. Further, Kako7) has investigated the modulation of carrier waves of arbitrary frequencies for all angles of propagation, so that the results obtained earlier are special cases. In this paper, we present an investigation of nonlinear wave

Propagation of solitary waves in a two ion species plasma with finite ion temperature

Abstract: Using a Korteweg-de Vries equation the author studies the propagation of ion acoustic solitary waves in a two ion species plasma. As the dispersion relation presents two acoustic branches with quite different phase velocities, two types of soliton can propagate: the slow one which is subsonic with respect to one ion mode and supersonic to the other, has greater amplitude and smaller width than the fast one.

Scattering of Lattice Waves by Static Strain Fields in Crystals

Abstract: On the basis of nonlinear elasticity theory, the scattering of lattice waves by a static strain field has been treated with special consideration of the elastic anisotropy of wave-propagating medium. A general form for the wave equation in strained medium was derived, and the scattered waves were determined by means of perturbation method by adopting the Born approximation. The Green's function method was conveniently used to determine the displacement of the scattered waves. The general method was applied to the case of scattering of lattice waves incident normally on a screw dislocation in a cubic crystal. The results of the calculation showed that the scattering was very anisotropic with regard to the incident direction and the scattering angle of the waves. It was found that, contrary to the dominance of purely forward scattering in isotropic medium, obliquely forward scattering occurred intensively in crystals.

Linear ion acoustic waves in a density gradient

Abstract: Both the experimental and theoretical behavior of linear ion acoustic waves in density gradients formed in a collisionless discharge plasma have been studied. The experiment and the theory both show a strong spatial growth of the density perturbation produced by the wave when the wave propagates in the direction of increasing density and a damping when the wave propagates in the direction of decreasing density. Theoretically, the growth and damping rates are found to be proportional to n01/2, where n0 is the local unperturbed density. By using the measured density profile, good agreement is found between experiment and the linearized fluid theory. Although the wave amplitude n1, itself, decreases as the wave propagates into a region of lower density, the relative amplitude n1/n0 increases. This can be expected to lead to wave steepening and shock‐like behavior, as noted previously by others. The work reported here is mainly concerned with the range where the wavelength is smaller than the characteristic l...