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Showing papers on "Longitudinal wave 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


Journal ArticleDOI
TL;DR: In this paper, the spacings of some cusps formed under reflective wave conditions both in the laboratory and in certain selected natural situations are shown to be consistent with models hypothesizing formation by either (1) subharmonic edge waves (period twice that of the incident waves) of zero mode number or (2) synchronous edge waves of low mode.
Abstract: Genetically, beach cusps are of at least two types: those linked with incident waves which are surging and mostly reflected (reflective systems) and those generated on beaches where wave breaking and nearshore circulation cells are important (dissipative systems). The spacings of some cusps formed under reflective wave conditions both in the laboratory and in certain selected natural situations are shown to be consistent with models hypothesizing formation by either (1) subharmonic edge waves (period twice that of the incident waves) of zero mode number or (2) synchronous (period equal to that of incident waves) edge waves of low mode. Experiments show that visible subharmonic edge wave generation occurs on nonerodable plane laboratory beaches only when the incident waves are strongly reflected at the beach, and this observation is quantified. Edge wave resonance theory and experiments suggest that synchronous potential edge wave generation can also occur on reflective beaches and is a higher-order, weaker resonance than the subharmonic type. In dissipative systems, modes of longshore periodic motion other than potential edge waves may be important in controlling the longshore scale of circulation cells and beach morphologies. On reflective plane laboratory beaches, initially large subharmonic edge waves rear-rage sand tracers into shapes which resemble natural beach cusps, but the edge wave amplitudes decrease as the cusps grow. Cusp growth is thus limited by negative feedback from the cusps to the edge wave excitation process. Small edge waves can form longshore periodic morphologies by providing destabilizing perturbations on a berm properly located in the swash zone. In this case the retreating incident wave surge is channelized into breeches in the berm caused by the edge waves, and there is an initially positive feedback from the topography to longshore periodic perturbations.

472 citations


Journal ArticleDOI
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


Journal ArticleDOI
TL;DR: In this article, the authors derived expressions for speed and attenuation of compressional waves travelling normal to the boundaries of a laminated medium which consists of alternating layers of two fluid-saturated porous solids.
Abstract: Expressions are derived for speed and attenuation of compressional waves travelling normal to the boundaries of a laminated medium which consists of alternating layers of two fluid‐saturated porous solids. Fluid flow across boundaries is taken into account through approximate expressions, applicable at low frequencies, derived through extension of the approach used by Gassmann. Calculations show that when one of the saturating fluids is gas, substantial dispersion and extreme attenuation may result.

265 citations


Journal ArticleDOI
TL;DR: In this paper, the effects of a baroclinic current on inertial internal waves at constant frequency were investigated, primarily through use of the method of characteristics, and the effect of the slope of an isopycnal is of the same order of magnitude as the slopes of the characteristics.
Abstract: Several effects of a baroclinic current on inertial‐internal waves at constant frequency are investigated, primarily through use of the method of characteristics. The special case of waves propagating transverse to a baroclinic current is considered. When the slope of an isopycnal is of the same order of magnitude as the slope of the characteristics, appreciable asymmetries are induced in the characteristics, the phase and group velocities, and the solution itself. These asymmetric effects are especially significant for waves at the low frequency end of the passband for free waves. Also, modifications occur to the passband, resulting in anomalously high and low frequency bands. The effective local inertial frequency, σf = [f(f+vx )]1/2, separates the normal and anomalously low frequency bands. Hence, the low frequency limit of the normal frequency band increases or decreases depending upon whether the horizontal shear in the mean flow is cyclonic or anticyclonic. In the anomalous frequency bands, the slop...

222 citations


Journal ArticleDOI
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.

220 citations


Journal ArticleDOI
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.

164 citations


Journal ArticleDOI
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.

149 citations


Journal ArticleDOI
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.

139 citations




Journal ArticleDOI
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.

Journal ArticleDOI
TL;DR: In this paper, the cyclotron wave instability in the corona for Bernstein modes and plasma waves in a hybrid band have been used to interpret zebra-pattern phenomena, and two models of the generation region of parallel drifting bands are considered: the point source localized at the apex of the magnetic trap and the model of a distributed source extended along the magnetic flux tube.
Abstract: The results of investigation of the cyclotron wave instability in the corona for Bernstein modes and plasma waves in a hybrid band have been used to interpret zebra-pattern phenomena. Two models of the generation region of parallel drifting bands are considered: the model of the point source localized at the apex of the magnetic trap and the model of a distributed source extended along the magnetic flux tube. In the first model it is assumed that a harmonic character of zebrapattern appears either in coalescence of excited Bernstein modes at different harmonics of the gyrofrequency or in coalescence of these modes with plasma waves excited in the hybrid band. In the latter case if the magnetic field changes in time a pulsating generation regime occurs. In the second model, the emission bands appear in the regions of double plasma resonance as a result of coalescence of longitudinal waves excited in the hybrid band. Estimations of the magnetic field and the nonequilibrium component density necessary for the zebra-pattern to generate are presented.

Journal ArticleDOI
TL;DR: In this paper, the bow shock crossing data were used to study 34 bow shock crossings observed from 5 to 16 earth radii upstream of the average bow shock location, and the wave polarization for the low-frequency waves is right-handed in relation to the average field direction when the observer moves from the upstream to downstream direction but is left-handed when moving in the opposite sense.
Abstract: Explorer 43 data were used to study 34 bow shock crossings observed from 5 to 16 earth radii upstream of the average bow shock location. Waves with periods of 6 to 130 s having amplitudes up to delta-B/B = 1 were detected. Wave polarization for the low-frequency waves is right-handed in relation to the average field direction when the observer moves from the upstream to downstream direction but is left-handed when the observer moves in the opposite sense. This fact identified the waves as standing whistler waves in the coordinate system of the shock. The waves are in agreement with collisionless low Mach number laminar shock theory. When the measured parameters were used to calculate theoretical wavelengths, the observed wave frequencies could be used to calculate velocities for the shock-wave coordinate system past the spacecraft; such velocities are mostly between 10 and 30 km/s. It is suggested that the higher-frequency propagating whistler waves may evolve from the standing whistler waves through a decay instability.

Journal ArticleDOI
TL;DR: In this article, the behavior of the long period waves (greater than one day) or planetary waves and of the tidal components has been studied and a striking similarity appears between the planetary waves at Obninsk and Garchy, and a phase shift between the two determinations has been noticed indicating a longitudinal propagation of these motions.

Journal ArticleDOI
TL;DR: In this paper, a new class of exact standing-wave solutions of the Maxwell cold-plasma equations with fixed ions was described, where the waves are transverse and circularly polarized.
Abstract: A new class of exact standing-wave solutions of the Maxwell cold-plasma equations with fixed ions is described. The waves are transverse, and circularly polarized. These solutions permit an analytical treatment of intense wave penetration into inhomogeneous plasmas with fixed ions.

Journal ArticleDOI
TL;DR: In this paper, the nonstationary evolution of nonlinear Langmuir waves is considered and the process of soliton formation is studied in the case where the perturbation propagates with a speed close to that of sound.
Abstract: The nonstationary evolution of nonlinear Langmuir waves is considered. In particular the process of soliton formation is studied in the case where the perturbation propagates with a speed close to that of sound. The influence of electron collisions on the motion of the soliton is also described.

Book
01 Jan 1975
TL;DR: In this article, a theory of propagating and standing internal waves over a horizontal ocean floor is proposed. But it does not consider the secondary effects of the internal waves on the ocean floor.
Abstract: : ;Contents: Observations and analysis of internal waves; Generation of internal waves; Theory of propagating and standing internal waves over a horizontal ocean floor; Secondary effects.

Journal ArticleDOI
TL;DR: In this paper, a statistical description of the dynamics of an ensemble of plane waves in nonlinear and strongly dispersive media is derived and a modulational instability, a second sound wave, and a localized group of waves are obtained from the description.
Abstract: A statistical description of the dynamics of an ensemble of plane waves in nonlinear and strongly dispersive media is derived. A modulational instability, a second sound wave, and a localized group of waves are obtained from the description. The results apply to the dynamics of many optical waves in strongly dispersive dielectric media with the Kerr effect as well as plasma waves for which decays or the wave particle interactions are prohibited.

Journal ArticleDOI
TL;DR: In this paper, the dispersion relations for Alfven waves with exp(jmϑ) azimuthal dependency are calculated for a cylindrical, cold, collisionless plasma.
Abstract: The dispersion relations for Alfven waves with exp(jmϑ) azimuthal dependency are calculated for a cylindrical, cold, collisionless plasma. If the electron inertia term is included in the dielectric tensor, then, in a bounded plasma, there are two transverse wavenumbers for each axial wavenumber. The phase velocities for m=0, ±1 fast and slow waves are calculated for different vacuum thicknesses between the uniform plasma and the metal walls. It is found that m=0 and −1 fast waves each experience a cutoff below a given frequency, but the m=+1 fast wave can propagate even at very low frequencies provided the vacuum layer is of sufficient thickness. The calculations are shown to agree with previously reported experimental results.

Journal ArticleDOI
TL;DR: In this article, the excitation of lower-hybrid waves by a multiple-ring slow-wave structure (four waves, λ=23 cm) in a magnetized plasma was reported.
Abstract: We report the excitation of lower-hybrid waves by a multiple-ring slow-wave structure (four waves, λ=23 cm) in a magnetized plasma. Wavelengths measured parallel and perpendicular to the magnetic field were in agreement with the theoretical dispersion relation. The waves propagated in a packet defined by the axial length of the slow-wave structure.

Journal ArticleDOI
TL;DR: In this paper, a large-volume laboratory plasma is filled with Whistler waves launched from an electric dipole of length L in a large volume laboratory plasma, and the radiation pattern narrows and forms a duct of diameter approximately equal to L. The observed nonlinear effects are explained by waveparticle interactions.
Abstract: Whistler waves are launched from an electric dipole of length L in a large-volume laboratory plasma. With increasing wave amplitude, the radiation pattern narrows and finally forms a duct of diameter approximately equal to L. The ducted waves propagate nearly undamped. The observed nonlinear effects are explained by wave-particle interactions.

Journal ArticleDOI
TL;DR: In this paper, a monochromatic unidirectional wave train, incident on a plane beach and strongly reflected there, is shown to transfer energy to edge waves of lower frequency through a weak nonlinear interaction.
Abstract: A monochromatic unidirectional wave train, incident on a plane beach and strongly reflected there, is shown to transfer energy to edge waves of lower frequency through a weak nonlinear interaction. For any angle of wave incidence the most readily excited edge wave perturbation consists of two low-mode progressive edge waves, generally having different frequencies and wave numbers, traveling in opposite directions along the beach. Standing edge waves, which might form stationary morphologic features with a regular longshore rhythm, are theoretically only excited when the primary surface waves are normally incident. However, edge waves generated by almost normally incident primary waves may be linked to features which slowly migrate along shore. On beaches bounded by headlands or jetties the progressive edge waves excited would be reflected at both ends, forming a complex pattern of standing waves. For beaches bounded at one end, only one of the edge waves would be standing. Regular beach cusps would therefore be expected in the vicinity of barriers. These cusps should decrease in relief with increasing distance from the obstacle as the reflected edge wave, which is not being actively forced, dies away due to viscous dissipation and further nonlinear interactions. Intriguingly, the cusps should have slightly different wavelengths on either side of the obstacle.

Patent
21 Feb 1975
TL;DR: In this article, an attenuator in the oscillatory circuit causes its operation to be marginally oscillatory whereby small changes in the amplitude of the rf waves caused by any perturbations in the ultrasonic waves produce relatively large changes in amplitude thereof.
Abstract: Apparatus for sensing particles in a fluid medium comprising an ultrasonic resonant cavity for containing a fluid medium. A first transducer on one side of the cavity continuously propagates thereacross ultrasonic compressional waves whose phase and amplitude are perturbed by the presence of particles in the fluid medium. A second transducer positioned on the opposite side of the cavity from the first transducer substantially parallel to and in registry therewith receives the ultrasonic waves and converts them to rf electric waves of the same frequency, the rf electric waves having their phases and amplitudes modulated in response to any perturbations in the ultrasonic waves. The rf waves are amplified and fedback to the first transducer thereby to establish an oscillatory circuit. An attenuator in the oscillatory circuit causes its operation to be marginally oscillatory whereby small changes in the amplitude of the rf waves caused by any perturbations in the ultrasonic waves produce relatively large changes in the amplitude thereof. A detector responsive to perturbations in the rf wave demodulates the amplified rf wave to produce signals indicative of the presence of particles in the fluid medium. Thus, enhanced sensitivity to small changes in the ultrasonic properties of the fluid medium caused by the presence of particles therein is achieved.

Journal ArticleDOI
TL;DR: In this article, the authors show that wind waves are accompanied by the wind drift surface current with large velocity shear and with horizontal variation of velocity relative to the wave profile, making a downward flow there, even though the wave is not breaking.
Abstract: Wind-wave tunnel experiments reveal, by use of techniques of the flow visualization, that wind waves are accompanied by the wind drift surface current with large velocity shear and with horizontal variation of velocity relative to the wave profile. The surface current converges from the crest to a little leeward face of the crest, making a downward flow there, even though the wave is not breaking. Namely, wind waves are accompanied by forced convections relative to the crests of the waves. Since the location of the convergence and the downward flow travels on the water surface as the crest of the wave propagates, the motion as a whole is characterized by turbulent structure as well as by the nature of water-surface waves. In this meaning, the term of real wind waves is proposed in contrast with ordinary water waves. The study of real wind waves will be essential in future development of the study of wind waves.

Journal ArticleDOI
TL;DR: In this paper, the structures and the behaviors of shock waves propagating through a gas and solid particle mixture are studied by shock-tube experiments and by two methods of wave analysis, and the analysis by the method of characteristics is satisfactorily applied to give a good explanation of the observed process whereby a shock wave decays to a weak wave with continuous wave form.
Abstract: The structures and the behaviors of shock waves propagating through a gas and solid particle mixture are studied by shock-tube experiments and by two methods of wave analysis. The shock waves concerned are incident on the mixture dispersed uniformly in downstream part of the driven section. Pressures and shock velocities are measured under the condition that the particle loading ratio and the shock Mach number are both less than two. The final equilibrium pressures behind the waves and the velocities of the fully decayed shock fronts agree well respectively with the results of the usual shock theory on the mixture and those of the model analysis on a perfect "effective" gas. The analysis by the method of characteristics is satisfactorily applied to give a good explanation of the observed process whereby a shock wave decays to a weak wave with continuous wave form. And, the authors point out some problems relating to the relaxation process and some inconsistencies of the "effective" gas theory when analyzing the unsteady wave motions.

Patent
Jun Kubota1, Soji Sasaki1
01 Jul 1975
TL;DR: In this article, a hard object to be inspected is sector-scanned with a supersonic wave beam with a variable-angle beam probe in direct contact with the object.
Abstract: A supersonic or ultrasonic wave flaw detector in which acoustic boundaries of flaws and/or abnormality of materials within an object to be inspected is detected by supersonic or ultrasonic waves and the position and shape of such a flaw and/or abnormality are displayed. A hard object to be inspected is sector-scanned with a supersonic wave beam with a variable-angle beam probe in direct contact with the object. In a range of comparatively small incident angles at which the longitudinal wave mainly penetrates the object, sectional images due to echo signals of the longitudinal wave are displayed on a display screen with scanning lines representative of the transmission speed and direction of the longitudinal wave. In the range of large incident angles where the shear wave penetrates the object, on the other hand, sectional images due to the echo signals of the shear wave are displayed on the display screen with scanning lines representative of the transmission speed and direction of the shear wave. For this, the sweeping speed and direction for the display scanning lines are switched in accordance with the ranges of incident angles. The switched flaw detecting operation modes of longitudinal and shear waves thus combined covers a complete sectional image to be displayed on the display screen.


Book ChapterDOI
01 Jan 1975
TL;DR: The theory of nonlinear wave propagation in both bounded and semi-infinite dissipative media is followed from its origins in the theories of linear geometrical acoustics, simple waves, and acceleration fronts as discussed by the authors.
Abstract: : The development of the theory of nonlinear wave propagation in both bounded and semi-infinite dissipative media is followed from its origins in the theories of linear geometrical acoustics, simple waves, and acceleration fronts. In Part I, Sections 2 to 5, we consider examples in which only one component wave is excited and describe the effects of three types of dissipative mechanisms on unidirectional waves. In Part II, Sections 6 to 9 we consider nonlinear waves in media of finite extent. In general, more than one component wave is excited. The coupling between the interaction and distortion of the different components is described. The effect of radiation from the boundaries is included for both transient and forced, time-periodic motions.

Journal ArticleDOI
TL;DR: A relation connecting the reflexion and transmission coefficients for scattering of water waves by a fixed body with the far-field radiated waves due to forced motions of the same body is derived in this article.
Abstract: A relation connecting the reflexion and transmission coefficients for scattering of water waves by a fixed body with the far-field radiated waves due to forced motions of the same body is derived Two alternative derivations are given, including a simple argument based on the analysis of an appropriate linear superposition of the two problems, and a more formal application of Green's theorem to the two potentials For bodies with horizontal symmetry, the transmission and reflexion coefficients are related to the phase angles of the far-field radiated waves associated with symmetric and antisymmetric forced motions of the body Some general conclusions follow for arbitrary symmetric bodies, and these are verified in specific cases by comparison with existing solutions The applicability of these relations to other types of wave problem is noted