Showing papers on "Wave propagation published in 1972"

Stationary solitary, snoidal and sinusoidal ion acoustic waves

Abstract: Stix's treatment of zero-damped electrostatic waves in a Maxwellian plasma is extended to the nonlinear regime. Stationary Bernstein-Greene-Krusk almodes which propagate with ion acoustic speed are constructed. This subclass consists of solitary, snoidal (=periodical waves, like ocean waves, which can be written in terms of Jacobian elliptic functions) and sinusoidal waves. A discrimination of those waves can be given by a single parameter, the steepness parameter, which contains nonlinearity, trapping of particles and dispersion. It turns out that Sadgeev's soliton represents a special case of the class solitons having the largest width and the lowest velocity. Hence a modified Korteweg-de-Vries equation must exist with a stronger nonlinearity.

Excitation of Plasma Waves by Two Laser Beams

Abstract: We analyze the effects of (i) the nonlinearity of the large-amplitude plasma wave, and (ii) the inhomogeneity of the plasma, on the excitation of the plasma wave by beating two laser beams.

Weak Nonlinear Dispersive Waves: A Discussion Centered Around the Korteweg–De Vries Equation

Abstract: This article is concerned with wave propagation processes where some balance occurs in the competition between a nonlinear effect and a higher order derivative effect which might be of a dispersive or a dissipative nature. The Burgers equation and the Korteweg–de Vries equation, which are prototype scalar nonlinear dissipative and dispersive equations, are shown to be fundamental to this study, even when quite general systems of equations are involved. The role of the solitary wave solution is shown to be central to the study which is applied to gravity waves, plasma waves and to waves in lattices. Both steady state solutions and initial value problems are reviewed together with questions of stability, existence and uniqueness.

Use of the three‐dimensional covariance matrix in analyzing the polarization properties of plane waves

Abstract: A technique for analyzing the polarization properties of plane waves that offers a number of advantages over methods currently used in the analysis of both ground and satellite observations of waves is developed. This technique reduces the computations required to find the wave normal vector, is less sensitive to common noise sources, and is amenable to analog implementation. The technique here is applied specifically to the analysis of a proton whistler, but it can also be used in most studies of ULF, ELF, and VLF magnetic-wave phenomena.

An Experimental and Theoretical Investigation of Elastic Wave Propagation in a Cylinder

Abstract: A high‐speed computer was used to investigate the problem of wave propagation in an isotropic elastic cylinder. Dispersion curves corresponding to real, imaginary, and complex propagation constants for the symmetric and the first four antisymmetric modes of propagation are given. The radial distributions of axial and radial displacements and of shear and normal stresses are given for the symmetric mode. By using a finite number of modes of propagation, an approximate solution is found for the problem of the L(0,1) mode impinging on a traction‐free interface. The reflection coefficient is determined in this way and the accompanying generation of higher order modes at the interface is shown to cause a high‐amplitude end resonance. Experimental results obtained by using the resonance method in conjunction with a long rod are presented to substantiate the calculated reflection coefficient and the frequency of end resonance. Phase velocities, based on measurements of the wavelength of standing waves and resonance frequencies, were obtained for the symmetric and first two antisymmetric modes. These measurements extend into the frequency range of more than one propagating mode. The rms deviation between theoretical and experimental results is in general less than 0.2% with the exception of the dispersion curve for the L(0,2) mode which deviates by 0.7%.

Analysis of the resistance increase in waves of a fast cargo ship

Abstract: A new method to calculate the added resistance of a ship in longitudinal waves is discussed. For the particular case of a fast cargo-ship the calculated values are compared with experimental results, and a satisfactory agreement is shown. In addition the experiments with the considered shipform confirm that added resistance varies as the squared wave height for constant speed and wave length.

Propagation and Amplification of Rayleigh Waves and Piezoelectric Leaky Surface Waves in LiNbO3

Abstract: Velocities and attenuations of piezoelectric leaky surface waves in LiNbO3 are analyzed. As a result, we have found that the effective electromechanical coupling coefficient of the leaky surface wave propagating along the X axis of a 64° rotated Y‐cut plane is very large, K2 = 0.113, and the attenuation of this wave, caused by radiation of the energy into the solid, is 0.036 dB/wavelength for a free surface and goes to zero for a metalized surface. Moreover, K2 of the elastic surface wave for a 130° rotated Y‐cut, X propagation, is found to be larger than that for a Y cut, Z propagation. The theory is verified experimentally. The theoretical analysis and experiments on amplification are performed for these types of waves. In an experiment utilizing the leaky surface wave, net terminal gain of 13 dB/cm is observed for the interaction between the carrier in 200‐Ω cm Si wafer (0.3×3×10 mm), separately mounted on a LiNbO3 surface, and the leaky surface wave. The air gap between the Si wafer and LiNbO3 single crystal is about 0.5 mμ.

Theory of Wave Propagation Along a Thin Wire Parallel to An Interface

Abstract: A solution is given for the boundary value problem of a wave propagating along a thin wire parallel to the interface between two homogeneous half-spaces. A general modal equation is derived for the propagation constant of the transmission current on the wire. It is shown how this result reduces to earlier known solutions obtained under more restrictive conditions.

Observations of running penumbral waves.

Abstract: Quiet sunspots with well-developed penumbrae show running intensity waves with period running around 300 sec. The waves appear connected with umbral flashes of exactly half the period. Waves are concentric, regular, with velocity constant around 10 km/sec. They are probably sound waves and show intensity fluctuation in H alpha centerline or wing of 10 to 20%. The energy is tiny compared to the heat deficit of the umbra.

Fluctuating magnetic fields in the magnetosphere. II - ULF waves.

Abstract: At the present time the existing satellite observations of ULF waves suggest that the level of geomagnetic activity controls the types of waves which occur within the magnetosphere. Consequently, we consider separately quiet times, times of magnetospheric substorms, and times of magnetic storms. Within each of these categories, there are distinctly different wave modes distinguished by their polarization: either transverse or parallel to the ambient field. In addition, these wave phenomena occur in distinct frequency bands. In terms of the standard nomenclature of ground micropulsation studies ULF wave types observed in the magnetosphere include quiet time transverse - Pc 1, Pc 3, Pc 4, Pc 5; quiet time compressional - Pc 1 and Pi 1; substorm compressional Pi 1 and Pi 2; storm transverse - Pc 1; storm compressional Pc 4, 5.

Gravity Waves in the Atmosphere

Abstract: Atmospheric gravity waves similar to waves that occur on the surface of a body of water have been known since the nineteenth century, but their significance for the study of atmospheric dynamics has been realized only in the past ten years

Parametric Excitation of Electromagnetic Waves

Abstract: Electromagnetic waves propagating along a dc magnetic field are shown to excite parametrically decay, purely growing, modulational and beat wave instabilities. Particular attention is given to whistler parametric instabilities, including a discussion of their nonlinear development and saturation.

Methods of determining electron concentrations in the magnetosphere from nose whistlers

Abstract: Whistler propagation in the magnetosphere was studied in detail to find accurate and economical means of determining the path latitude and the electron concentration along the path from whistler parameters of nose frequency and travel time at the nose. Longitudinal propagation in field aligned whistler ducts of cold plasma was assumed, and the earth's magnetic field was approximated by a centered dipole. The effects of whistler propagation in the earth-ionosphere waveguide and through the conjugate ionospheres were treated as small perturbations. Several alternative methods are described so that the most economical method may be chosen depending on the desired accuracy and the availability of a computer or a calculator.

IMPROVED KORTEWEG--deVRIES EQUATION FOR ION-ACOUSTIC WAVES.

Abstract: The Korteweg‐deVries equation describing nonlinear ion‐acoustic waves in a plasma with finite ion temperature is derived and the temperature dependences of soliton width and speed are obtained.

Theory and design of periodic couplers.

Abstract: The theory of periodic couplers is examined from the point of view of the reciprocity theorem and a modified Born scattering approach. Design equations for several coupler configurations are presented. Efficiency and aperture size calculations are compared with previously published data for grating and Bragg couplers.

On the interaction of surface and internal waves

Abstract: The steady-state interaction between surface waves and long internal waves is investigated theoretically using the radiation stress concepts derived by Longuet-Higgins & Stewart (1964) (or Phillips 1966). It is shown that, over internal wave crests, those surface waves for which cg0cosϕ0 > ci experience a change in direction of propagation towards the line of propagation of the internal waves and their amplitudes are increased. Here cg0 is the surface-wave group speed at U = 0, ϕ0 is the angle between the propagation direction of the surface waves at U = 0 and the propagation direction of the internal waves, and ci is the phase speed of the internal waves. If cg0cos ϕ0 < ci the direction of the surface waves is turned away and their amplitudes are decreased. Over troughs the opposite effects occur.At positions where the local velocity of surface-wave energy transmission measured relative to the internal wave phase velocity is zero, i.e. cg + U − ci = 0, there is a singularity in the energy of the surface waves with resulting infinite amplitudes. It is shown that at these critical positions two wavenumbers which were real and distinct on one side coalesce and become complex on the other. The critical positions are thus shown to be barriers to the propagation of those wave-numbers. It is also shown that there is a critical position representing the coalescence of three wavenumbers. Surface-wave crest configurations are shown for three numerical examples. The frequency and direction of propagation of surface waves that exhibit critical positions somewhere in an internal wave field are shown as a function of the maximum horizontal surface current. This is compared with measurements of wind waves that have been reported elsewhere.

Finite Amplitude Waves on Aircraft Trailing Vortices

Abstract: Numerical methods are used to study the growth of waves of finite amplitude on a pair of parallel infinite vortices. The vortices are treated as lines except in so far as the detailed structure of the core is needed to remove consistently the singularity in the line integrals for the velocities of the vortices. It is shown that the vortices eventually touch and the shape of the wave at this instant is calculated. The wave is quite distorted at this instant, but it is shown that its gross properties are given roughly by linear theory.

Statistical Theory of Wave Propagation in a Random Medium and the Irradiance Distribution Function

Abstract: The complete statistical description of the waves in a random medium can be obtained from the characteristic functional or the cumulant functional of the wave function. The basic equations of these functionals are found first for the gaussian medium and then for the nongaussian medium. As an application of those equations, the approximate equations of the arbitrary-order coherence functions are derived, which are found to be equivalent to those recently obtained by several authors using different methods. The operational method is introduced to solve the equation of the νth-order moment of the irradiance, and an exact solution is obtained for the particular correlation function of the medium, assuming the gaussian form of the incident wave. The irradiance probability-density function is obtained without approximation by the use of the νth-order moment of irradiance for this particular medium, and is found to be exactly the Rice–Nakagami distribution with respect to the log irradiance. This distribution approaches the log-normal distribution in the outside domain of the wave beam, and is also checked in several points. Finally, the operator representation of the physical variables is introduced, and it is shown that the various equations, e.g., the wave equation and the energy-conservation equation, in the statistical system of the wave plus the random medium can be represented by the same equations as the corresponding equations in the deterministic medium. The discussion is also extended on the basis of DeWolf’s result for the irradiance-distribution function.

The propagation of a weak nonlinear wave

Abstract: We consider the propagation of a weak nonlinear wave whose energy is concentrated in a narrow band of wavenumbers in a fluid which is both dispersive and dissipative. We use the small amplitude equations of Whitham's theory of slowly varying wave trains, modified slightly to include dissipation, to show that the modulation of the wave may be described by a nonlinear Schrodinger equation. For long waves which are purely dispersive we obtain the Kortewegde Vries equation, and for long waves which are dissipative we obtain Burgers’ equation by suitable transformations of the nonlinear Schrodinger equation. We mention the problem of Stokes waves in deep water and comment briefly upon invariant far-field theory.

Dynamic response of materials to intense impulsive loading

Abstract: The study of the dynamic response of materials, primarily solids, to intensive impulse loadings, both mechanical impact and thermodynamic energy input, for durations in the order of microseconds is discussed in detail. The subjects discussed include: basic conservation laws from the classical fluid mechanics point of view; the propagation of steady discontinuous stress waves; shock waves as studied from the thermodynamics and physics Point of view; constitutive relations and wave propagation in solids from a modern continuum mechanics viewpoint; method of characteristics in unsteady material response problems. introduction to numerical analysis; experimental techniques and instrumentation; and applications dealing with shock waves and high-pressure dynamic material response for scientific, engineering, and military purposes. (LCL)

Finite-Amplitude Baroclinic Wave Packets

Abstract: A theory is presented for the propagation of wave packets in a slightly unstable baroclinic shear flow in a quasi-geostrophic two-layer model on the beta plane. The theory for inviscid motions is considered and packet solutions resembling solitary waves are found. It is shown that the propagation speed of the packet, which is a function of its amplitude, exceeds the most naturally defined group velocity. A physical explanation is presented and it is suggested that the enhancement of the signal velocity above the group velocity is a general property of systems possessing linear instability and nonlinear stability.

The transmission of surface waves through a gap in a vertical barrier

Abstract: The two-dimensional configuration is considered of a fixed, semi-infinite, vertical barrier extending downwards from a fluid surface and having, at some depth, a gap of arbitrary width. A train of surface waves, incident on the barrier, is partly transmitted and partly reflected. The velocity potential of the resulting fluid motion is determined by a reduction procedure and also by an integral equation formulation. It is shown that the two methods lead to the same Riemann–Hilbert problem. Transmission and reflexion coefficients are calculated for several values of the ratio gap width/mean gap depth.

Electromagnetic Wave Propagation Along a Buried Insulated Wire

Abstract: Propagation along a thin dielectric coated wire parallel to the interface between two homogeneous half-spaces is considered. The solution accounts for the presence of the interface provided the coa...

Electrostatic Instability of Ring Current Protons Beyond the Plasmapause During Injection Events

Abstract: The stability of ring current protons with an injection spectrum modeled by an m = 2 mirror distribution function was examined for typical ring current parameters It was found that the high frequency loss cone mode can be excited at wave numbers K lambda sub Di about = to 01 to 05, at frequencies omega about = to (02 to 06) omega sub pi and with growth rates up to gamma/omega about = to 003 These waves interact with the main body of the proton distribution and propagate nearly perpendicular to the local magnetic field Cold particle partial densities tend to reduce the growth rate so that the waves are quenched at or near to the plasmapause boundary Wave e-folding lengths are comparable to 01 R sub e, compared to the value of about 4 R sub e found for ion cyclotron waves at the same plasma conditions