Showing papers on "Wave propagation published in 1975"
Book•
01 Jan 1975
TL;DR: In this article, a comprehensive study of elastic wave propagation in solids is presented, ranging from the theory of waves and vibrations in strings to the three-dimensional theory of elastic waves in thick plates.
Abstract: The book presents a comprehensive study of elastic wave propagation in solids. Topics covered range from the theory of waves and vibrations in strings to the three-dimensional theory of waves in thick plates. The subject is covered in the following chapters: (1) waves and vibrations in strings, (2) longitudinal waves in thin rods, (3) flexural waves in thin rods, (4) waves in membranes, thin plates and shells, (5) waves in infinite media, (6) waves in semi-infinite media, (7) scattering and diffraction of elastic waves, and (8) wave propagation in plates and rods. Appendices contain introductory information on elasticity, transforms and experimental techniques. /TRRL/
3,359 citations
424 citations
TL;DR: The theoretical and observational evidence concerning the global propagation of atmospheric gravity waves is reviewed in this article, with special emphasis on the waves generated in the auroral zones, and it is concluded that the only natural sources of large-scale TIDs are in the ionospheric zones.
392 citations
TL;DR: In this article, the relationship between the bounding frequencies of propagation zones of mono-coupled periodic systems and the natural frequencies of the individual elements of which the system is composed is studied.
378 citations
TL;DR: In this article, the boundary conditions for the discrete wave equation are constructed using projection operators, and the separation of waves into ingoing and outgoing waves inherent in these boundary conditions greatly facilitates diagnostics.
354 citations
TL;DR: In this article, the effect of gravity waves on the observed Doppler shift of a sinusoidal electromagnetic signal transmitted to, and transponded from, a distant spacecraft is investigated.
Abstract: A calculation is made of the effect of gravity waves on the observed Doppler shift of a sinusoidal electromagnetic signal transmitted to, and transponded from, a distant spacecraft. We find that the effect of plane gravity waves on such observations is not intuitively immediate and in fact can have surprisingly different spectral signatures for different spacecraft directions and distances. We suggest the possibility of detecting such plane waves by simultaneous coherent Doppler tracking of several spacecraft.
294 citations
TL;DR: In this paper, the nature of the characteristic wave motions is studied, and a characteristic receptance matrix for a characteristic wave is defined, and the equations governing the reflection process are set up, and used to formulate the equations for the natural frequencies and modes of a finite periodic system with arbitrary boundaries.
268 citations
TL;DR: In this article, a model equation is derived which approximately describes the propagation of periodic surface waves in water of slowly varying depth, and numerical solutions to the model equation are obtained for the scattering of an incident plane wave by a conical island.
Abstract: A model equation is derived which approximately describes the propagation of periodic surface waves in water of slowly varying depth. Numerical solutions to the model equation are obtained for the scattering of an incident plane wave by a conical island.
266 citations
TL;DR: In this article, the effects of meridional circulation and the diffusion process on the propagation nature of the dynamo waves are estimated, and the importance of this theorem is stressed for understanding the solar cycle and for inferring the rotational law of the interior of the Sun.
Abstract: Dynamo waves, as solutions of the dynamo equations governing the solar cycle, propagate along isorotation surfaces inside the Sun. This theorem, universal in most dynamo models of the solar cycle, is proven analytically, and the nature of the propagation is analyzed. The effects of meridional circulation and the diffusion process on the propagation nature of the dynamo waves are estimated. The importance of this theorem is stressed for understanding the solar cycle and for inferring the rotational law of the interior of the Sun. (AIP)
251 citations
TL;DR: In this article, the amplitude of a 0.575-Hz plunger-generated wave was measured in a wave tank as a function of air friction velocity and plunger wave amplitude.
Abstract: The modulation in backscattered power from wind-generated waves due to the presence of a 0.575-Hz plunger-generated wave has been measured in a wave tank as a function of air friction velocity and plunger wave amplitude. The measurements were made at 9.375 GHz, a depression angle of 45° and vertical polarization. The straining of the wind waves is treated by a first-order perturbation of the Boltzmann transport equation and the scattering is calculated from a simple application of composite surface scattering theory utilizing first-order Bragg scattering. The theory predicts a characteristic relaxation behavior for the wind-speed dependence of the components of the modulation amplitude in phase and out of phase with the horizontal component of orbital velocity of the plunger wave. This relaxation behavior is closely followed by the observed modulation amplitudes for air friction velocities less than about 40 cm sec−1, i.e., winds less than about 7 m sec−1.
TL;DR: In this paper, a number of exact relations for periodic water waves of finite amplitude in water of uniform depth were proved and the mean fluxes of mass, momentum and energy were shown to be equal to 2T(4T-3F) and (3T-2V) crespectively, where T and V denote the kinetic and potential energies and c is the phase velocity.
Abstract: A number of exact relations are proved for periodic water waves of finite amplitude in water of uniform depth. Thus in deep water the mean fluxes of mass, momentum and energy are shown to be equal to 2T(4T—3F) and (3T—2V) crespectively, where T and V denote the kinetic and potential energies and c is the phase velocity. Some parametric properties of the solitary wave are here generalized, and some particularly simple relations are proved for variations of the Lagrangian The integral properties of the wave are related to the constants Q, R and S which occur in cnoidal wave theory. The speed, momentum and energy of deep-water waves are calculated numerically by a method employing a new expansion parameter. With the aid of Pade approximants, convergence is obtained for waves having amplitudes up to and including the highest. For the highest wave, the computed speed and amplitude are in agreement with independent calculations by Yamada and Schwartz. At the same time the computations suggest that the speed and energy, for waves of a given length, are greatest when the height is less than the maximum. In this respect the present results tend to confirm previous computations on solitary waves.
TL;DR: In this article, the propagation of ion-acoustic waves (IAW) in a double-electron- temperature plasma is investigated both experimentally and theoretically, and it is found that the presence of even a small fraction of the lower electron- temperature component can dominate the behavior of the waves.
Abstract: The propagation of ion-acoustic waves (IAW) in a double-electron- temperature plasma is investigated both experimentally and theoretically. It is found that the presence of even a small fraction of the lower-electron- temperature component can dominate the behavior of the waves. The results have important implications both for the use of IAW as a diagnostic tool for measuring electron temperature and for the interpretation of turbulent IAW spectra. (AIP)
TL;DR: In this article, some new dielectric waveguide structures suitable for millimeter-wave and optical integrated circuits are presented and a method of analyzing wave propagation in these guides is developed by assuming simple field distribution and approximating the various regions of the guides in terms of effective dielectrics constants.
Abstract: Some new dielectric waveguide structures suitable for millimeter-wave and optical integrated circuits are presented. A method of analyzing wave propagation in these guides is developed by assuming simple field distribution and approximating the various regions of the guides in terms of effective dielectric constants. The mathematical formulation utilized results in simple eigenvalue equations from which the dispersion characteristics of the waveguides are readily obtained. Experimental results are described and the agreement between theory and experiment is shown to be quite good.
Book•
01 Jan 1975
TL;DR: In this paper, the authors provide an introduction to the theory of propagation and the dynamics of mesoscale atmospheric masses and wave propagation in the field of radiophysics, as well as their role in the generation of clear air turbulence (CAT).
Abstract: Development in Atmospheric Science, 2
In recent years 'here has been increased
interest in mesoscale atmospheric waves as
newly developed atmospheric probes such as
radars and acoustic echo sounders have
made it possible to study these waves in
great detail. Numerous observations reported
in a rapidly expending literature on the
subject have demonstrated that these waves
are more than mere curiosities; in fact, they
can play an essential role in the generation of
some kinds of clear air turbulence (CAT), .
thus Creating a hazard to commercial aircraft;,
and they may be very important to the very
dynamics of the larger-scale atmospheric
circulation, This timely book provides the
interested meteorologist, radiophysicist. and
graduate student with a self-contained
introduction to the theory of propagation and
the dynamics of mesoscale atmospheric
waves.
TL;DR: In this article, a computer algorithm is presented which allows simultaneous consideration of selfphase modulation and dispersion for predicting temporal shape changes during the propagation of plane-wave intense light pulses.
Abstract: A computer algorithm is presented which allows simultaneous consideration of self‐phase modulation and dispersion for predicting temporal shape changes during the propagation of plane‐wave intense light pulses. The algorithm entails considering propagation alternately in regions where only one of the two above effects is operative. It is shown for clear materials that the parameters characterizing propagation are the nonlinear index change, the wavelength λ, the relaxation time of the nonlinearity, and the disperison parameter λ3(d2n/dλ2). The thickness of material over which a pulse will significantly reshape is found to be √λ times the geometric length of the pulse divided by the square root of the product of the dispersion parameter and the maximum nonlinear index. It is demonstrated that dispersion significantly modifies the self‐steepening concept of DeMartini, Townes, Gustafson, and Kelley. Numerical simulations of propagation in CS2 indicate that, after sufficient travel, a shock can form on the le...
TL;DR: In this paper, the Korteweg-de Vries equation in a multicomponent plasma that includes any number of positive and negative ions has been derived for the case of isothermal and non-isothermal electrons.
Abstract: The authors derive the Korteweg-de Vries equation in a multicomponent plasma that includes any number of positive and negative ions. The solitary wave solutions are also found explicitly for the case of isothermal and non-isothermal electrons.
TL;DR: In this paper, the S theory is proposed to limit the amplitude of the exponentially growing spin wave in ferromagnetic dielectric dielectrics by pairing of waves with equal and opposite wave vectors, which leads to the violation of phase relationships.
Abstract: The nonlinear stage of the parametric excitation of spin waves in ferromagnetic dielectrics is reviewed. The main nonlinear mechanism which limits the amplitude of the exponentially growing waves is the pairing of waves with equal and opposite wave vectors, which leads to the violation of phase relationships. This effect is described in terms of a Hamiltonian which is diagonal in the wave pairs; The corresponding approximation is called the S theory. Within the framework of this theory, the distribution of the excited waves in κ space is singular: the waves lie on individual lines or points. Consequences of the S theory and their experimental verification are discussed in detail. Collective oscillations of a spin-wave system and the origin of the observed self-modulation of their amplitude are also considered.
TL;DR: Garnet, H. and Armen, H., Evaluation of Numerical Time Integration Methods as Applied to Elastic-Plastic Dynamic Problems Involving Wave Propagation, Rept. RE-475, March 1974, Research Dept., Grumman Aircraft Corp., Bethpage, N.Y. as mentioned in this paper.
Abstract: 2 Garnet, H. and Armen, H., Evaluation of Numerical Time Integration Methods as Applied to Elastic-Plastic Dynamic Problems Involving Wave Propagation, Rept. RE-475, March 1974, Research Dept., Grumman Aircraft Corp., Bethpage, N.Y. 3 Stoodley, G. R. and Ball, D. J., Mathematical Background of Two Numerical Integration Techniques for Ordinary Differential Equations, Memo. RM-192, Oct. 1961, Research Dept, Grumman Aircraft Corp., Bethpage, N.Y. 4 Mantus, M., Lerner, E., and Elkins, W., "Landing Dynamics of the Lunar Excursion Module (Method of Analysis)," Rept. LED-5206A, Revised April 10, 1967, Grumman Aircraft Corp., Bethpage, N.Y. 5 Lerner, E. and Mantus, M., "Dynamics of Unsymmetric Landing," Rept. ADR 02-10-10-62-1, Jan. 1963, Grumman Aircraft Corp, Bethpage, N.Y. 6 Donnell, L. H., "Longitudinal Wave Transmission and Impact," Transactions of the ASME, Vol, 52, 1930, pp. 153-167. 7 DeJuhasz, K. J., "Graphical Analysis of Impact of Bars Stressed Above the Elastic Range," Journal of the Franklin Institute, Vol. 248, No. 2, Aug. 1949, pp. 113-142. 8 Davids, N. and Kumar, S., "A Contour Method for One Dimensional Pulse Propagation in Elastic-Plastic Materials," Proceedings of the Third U.S. National Congress of Applied Mechanics, Brown University, Providence, R.I., 1958, pp. 502-512. 9 Garnet, H. and Armen, H., One Dimensional Elastic-Plastic Wave Propagation and Boundary Reflections, Memo, Grumman Research Department, Bethpage, N.Y. (in preparation).
TL;DR: A broad review of the theoretical studies of the physical processes affecting the excitation, dissipation, and interaction of internal waves in the deep ocean is given in this article, where the authors present a broad overview of the literature.
Abstract: This paper is a broad review of the theoretical studies of the physical processes affecting the excitation, dissipation, and interaction of internal waves in the deep ocean.
TL;DR: In this article, it was shown that the small wave structure controls fluid resistance and transfer processes in the gas while the large wave structure controlled these same processes in a liquid film and that the form drag of the large waves contributed negligibly to the observed pressure drop in a gas phase.
Abstract: Two classes of random waves exist on falling films at flow rates of practical interest; large waves which carry the bulk of the liquid and small waves which cover the substrate. In this paper statistics of the large waves are presented and compared with existing theory. These waves are bimodal in character at ReL > 700. The form drag of the large waves is shown to contribute negligibly the observed pressure drop in the gas phase. It is thus concluded that the small wave structure controls the fluid resistance and transfer processes in the gas while the large waves control these same processes in the liquid film.
TL;DR: In this article, a detailed experimental and theoretical study into the response of a 2-layer, plane-stratified, low-loss dielectric earth is presented, and the experimental results are useful in turn in demonstrating the reliability of approximate theoretical solutions for the electromagnetic fields about the dipole obtained by normal mode and geometrical optics methods.
Abstract: The use of the radio interferometry method requires a detailed understanding of the nature of electromagnetic wave propagation in structures composed of materials with low electrical loss. This paper contains the results of a detailed experimental and theoretical study into the response of a 2-layer, plane-stratified, low-loss dielectric earth. The technique used to construct a scale model with microwave equipment to experimentally simulate the 2-layer structure response is discussed. The wave nature of the response derived from the theoretical investigations is used to interpret the features of the experimental results. The experimental results are useful in turn in demonstrating the reliability of approximate theoretical solutions for the electromagnetic fields about the dipole obtained by normal mode and geometrical optics methods. Such features as (1) the modification of the dipole radiation pattern seen when the antenna is placed at the interface between media of differing electrical properties, and (2) the development of guided and leaky modes in the layered structure are examined in detail.
TL;DR: In this article, two types of dispersion relations are experimentally shown to exist in an ion-beam-plasma system, and two normal modes, one unstable, are seen for beam velocities close to the ion-sound speed.
Abstract: Two types of dispersion relations are experimentally shown to exist in an ion-beam-plasma system. For beam velocities close to the ion-sound speed, two normal modes, one unstable, are seen. For larger beam velocities, the interferometer output exhibits beating between the three predicted stable normal modes, which are the "fast" and "slow" ion-beam modes and the plasma ion-acoustic wave.
TL;DR: In this paper, the condition of the Weber number of order one for the free surface is computed to the third-order accuracy of the shallow water parameter, and the development of a long monochromatic wave is analyzed by use of this equation.
Abstract: Long nonlinear waves on a thin fluid layer flowing down an inclined plane are investigated. For the condition of the Weber number of order one, the equation for the free surface is computed to the third‐order accuracy of the shallow water parameter. The development of a long monochromatic wave is analyzed by use of this equation. Near the upper branch of the neutral curve, the original steady flow is found to be supercritically stable and the amplitude of the monochromatic wave is determined. The stretching of the eigenfrequency by nonlinearity has no definite sign. For a comparatively large wavenumber, the wave velocity can be smaller than that of the linear wave. The nonexistence of the periodic wave in the region far from the upper branch of the neutral curve is discussed in connection with the temporally growing solution of the equation in order to determine the second harmonic.
TL;DR: In this paper, the authors derived coupled nonlinear partial differential equations, which describe a nonlinear interaction between short and long capillary-gravity waves on a liquid layer of uniform depth, by the derivative expansion method.
Abstract: Coupled nonlinear partial differential equations, which describe a nonlinear interaction between short and long capillary-gravity waves on a liquid layer of uniform depth, are derived by the derivative expansion method. The short and the long waves can exchange energy in a resonant manner, if the group velocity of the short wave is close to the phase velocity of the long wave. It is found that the long wave can take a form of rarefactive (convex downwards) solitary wave due to the resonant interaction. This should be compared with the well-known gravity wave soliton which is compressive (convex upwards) in the absence of the short wave.
TL;DR: In this article, the nonlinear distortion of the propagation cones of lower-hybrid waves is shown to be governed by the modified Korteweg-de Vries equation, which admits exact solutions of the multiple-soliton form.
Abstract: The nonlinear distortion of the propagation cones of lower-hybrid waves is shown to be governed by the modified Korteweg-de Vries equation. Since such an equation admits exact solutions of the multiple-soliton form, it is predicted that filamented cones sould be formed when large-amplitude lower-hybrid waves are excited in a plasma.
TL;DR: In this article, the propagation and radiation of electromagnetic waves from oscillating sources in a suddenly created plasma are studied in detail and field expressions are derived through the use of Laplace transformations.
Abstract: Propagation and radiation of electromagnetic waves from oscillating sources in a suddenly created plasma are studied in this investigation. Field expressions are derived through the use of Laplace transformations. The spatial distribution of sources is taken to be arbitrary but confined. Two cases are considered in detail: 1) plane wave propagation in a source-free region and 2) electric point dipole radiation. In the case of plane wave propagation, various aspects such as wave split, frequency shift, phase and group velocities, amplitude changes, power flows, and energy relations are discussed. In the case of electric dipole radiation, the electromagnetic fields and instantaneous radiated power are calculated and expressed in terms of Lommel functions of two variables. Asymptotic expressions and graphical results of numerical calculations of these quantities are presented. Many interesting properties of the spherical waves and power radiation are discussed.
01 Oct 1975
TL;DR: In this paper, the relativistic plane nonlinear waves were investigated: circularly polarized waves and electrostatic plasma oscillations propagating parallel to the magnetic field, relativists Alfven waves, linearly polarized transverse waves propagating in zero magnetic field and the extraordinary mode propagating at an arbitrary angle to magnetic field.
Abstract: Five relativistic plane nonlinear waves were investigated: circularly polarized waves and electrostatic plasma oscillations propagating parallel to the magnetic field, relativistic Alfven waves, linearly polarized transverse waves propagating in zero magnetic field, and the relativistic analog of the extraordinary mode propagating at an arbitrary angle to the magnetic field. When the ions are driven relativistic, they behave like electrons, and the assumption of an 'electron-positron' plasma leads to equations which have the form of a one-dimensional potential well. The solutions indicate that a large-amplitude superluminous wave determines the average plasma properties.
CNET1
TL;DR: In this paper, the role of wave particle interactions in the dynamics of magnetospheric particles is stressed and the concepts of optimum cold plasma density, critical energy, limiting flux, marginal stability, steady-state equilibrium are critically discussed.
Abstract: Recent space observations of waves, both electromagnetic and electrostatic, are reviewed and the role which they can play in the dynamics of magnetospheric particles is stressed. Wave particle interactions (WPI) in the exo- and intra-plasmaspheric media depend on the exact process of particle injection under the influence of magnetospheric electric fields, and on the spatial distribution of the cold plasma particles; these two aspects of the problem are studied to some extent. The concepts of optimum cold plasma density, critical energy, limiting flux, marginal stability, steady-state equilibrium are critically discussed. The non-linear aspects — both experimental and theoretical — of WPI's are reviewed and a special section is devoted to active experiments in space. An attempt is made to outline which kind of experiments could be made at high-latitudes, in conjunction with IMS spacecrafts, in order to arrive at a better understanding of magnetospheric processes involving waves and particles.