Showing papers on "Longitudinal wave published in 1978"

Waves in fluids

Abstract: Preface Prologue 1. Sound waves 2. One-dimensional waves in fluids 3. Water waves 4. Internal waves Epilogue Bibliography Notation list Author index Subject index.

Waves in the ocean

Abstract: Introduction. Free waves: Short wavelengths. Free waves: Long wavelengths. Free waves: Lateral boundary effects. Statistical and probabilistic methods. Wave interactions. Wave-current interactions: Critical layer absorption and stability of parallel flows. The generation and dissipation of waves. References. Author Index. Subject Index

Tsunamis -- the propagation of long waves onto a shelf

Abstract: The various aspects of the propagation of long waves onto a shelf (i.e., reflection, transmission and propagation on the shelf) are examined experimentally and theoretically. The results are applied to tsunamis propagating onto the continental shelf. A numerical method of solving the one-dimensional Boussinesq equations for constant depth using finite element techniques is presented. The method is extended to the case of an arbitrary variation in depth (i.e., gradually to abruptly varying depth) in the direction of wave propagation. The scheme is applied to the propagation of solitary waves over a slope onto a shelf and is confirmed by experiments. A theory is developed for the generation in the laboratory of long waves of permanent form, i.e., solitary and cnoidal waves. The theory, which incorporates the nonlinear aspects of the problem, applies to wave generators which consist of a vertical plate which moves horizontally. Experiments have been conducted and the results agree well with the generation theory. In addition, these results are used to compare the shape, celerity and damping characteristics of the generated waves with the long wave theories. The solution of the linear nondispersive theory for harmonic waves of a single frequency propagating over a slope onto a shelf is extended to the case of solitary waves. Comparisons of this analysis with the nonlinear dispersive theory and experiments are presented. Comparisons of experiments with solitary and cnoidal waves with the predictions of the various theories indicate that, apart from propagation, the reflection of waves from a change in depth is a linear process except in extreme cases. However, the transmission and the propagation of both the transmitted and the reflected waves in general are nonlinear processes. Exceptions are waves with heights which are very small compared to the depth. For these waves, the entire process of propagation onto a shelf in the vicinity of the shelf is linear . Tsunamis propagating from the deep ocean onto the continental shelf probably fall in this class.

An instability of finite amplitude circularly polarized Alfven waves

Abstract: A demonstration is presented that a finite-amplitude circularly-polarized Alfven wave is generally unstable in a MHD fluid. The wave decays by a four-wave coupling process in which the daughter waves are forward propagating random density and magnetic fluctuations and a backward-propagating magnetic wave. For parameters typical of the solar corona and the solar wind (thermal to magnetic energy density ratios between 0.1 and 1, and values between 0.1 and 0.9 for the ratio of magnetic energy density of the initial Alfven wave to that of the background magnetic field), large decay rates are found.

Gravity wave generation, propagation, and dissipation in the thermosphere

Abstract: This is the first in a series of papers examining large-scale gravity waves in the thermosphere and their ability to transfer energy from high to low latitudes during magnetic disturbances. The gravity wave source is assumed to be either the Lorentz force of auroral electrojet currents or else a heat input due to energetic particle precipitation or to Joule heating. It is pointed out that the characteristic vertical width of the gravity wave source should usually lie between 2 and 4 pressure scale heights, placing constraints on the vertical wavelengths and horizontal velocities of the generated waves. A simplified analytic model of small-amplitude wave generation by a current source shows how wave energy production depends on the temporal and spatial dimensions of the source, on the electric field strength, and on the electron density enhancement. The steep thermospheric temperature gradient in the vicinity of the source altitude strongly influences the properties of upward and downward propagating waves compared with waves generated in an isothermal atmosphere. Waves produced by the Lorentz force of Hall currents, by the Lorentz force of Pedersen currents, and by Joule heating are influenced quite differently by this temperature gradient. Because upgoing waves above the source are combinations of waves originally launched upward and waves originally launched downward but reflected around 110 km altitude, the mean effective source altitude is about 110 km for the far field response in the thermosphere. Large-scale traveling ionospheric disturbances observable at middle latitudes are most likely produced primarily by Pedersen, rather than Hall, currents. The temperature structure of the thermosphere generally causes gravity wave packets to refract upward; waves traveling with a horizontal component of velocity faster than 250 m/s and with an initial downward component of group velocity will always be reflected upward in the lower thermosphere. The effects of viscosity, heat conduction, and Joule dissipation tend to filter out shorter-period and slower moving waves from observation points at some distance from the source, so that only long-period fast moving waves can reach low latitudes from an auroral source. For example, a wave with a 94-min period moving horizontally at 605 m/s is largely dissipated by the time it has traveled 4000 km from a typical auroral source. A numerical simulation using a fairly realistic thermospheric model illustrates many of the points described from analytic considerations.

Modulational instability of finite-amplitude, circularly polarized Alfven waves

Abstract: The simple theory of the decay instability of Alfven waves is strictly applicable only to a small-amplitude parent wave in a low-beta plasma, but, if the parent wave is circularly polarized, it is possible to analyze the situation without either of these restrictions. Results show that a large-amplitude circularly polarized wave is unstable with respect to decay into three waves, one longitudinal and one transverse wave propagating parallel to the parent wave and one transverse wave propagating antiparallel. The transverse decay products appear at frequencies which are the sum and difference of the frequencies of the parent wave and the longitudinal wave. The decay products are not familiar MHD modes except in the limit of small beta and small amplitude of the parent wave, in which case the decay products are a forward-propagating sound wave and a backward-propagating circularly polarized wave. In this limit the other transverse wave disappears. The effect of finite beta is to reduce the linear growth rate of the instability from the value suggested by the simple theory. Possible applications of these results to the theory of the solar wind are briefly touched upon.

Exact solitary ion acoustic waves in a magnetoplasma

Abstract: It is shown that finite amplitude ion acoustic solitary waves propagating obliquely to an external magnetic field can occur in a plasma.

Modulus and Damping of Soils by the Resonant-Column Method

Abstract: The resonant-column method, a relatively nondestructive test employing wave propagation in cylindrical specimens, is used to obtain modulus and damping of soils as functions of vibratory strain amplitude and other factorssuch as ambient confining stress and void ratio. Descriptions of the apparatus, calibration procedures, testing procedures, and aids for data reduction are given for apparatus which propagate either rod compression waves or shear waves or both. Data reduction aids include graphs for a wide range of apparatus conditions and include a computer program that covers all admissable boundary conditions.

Finite amplitude solitary Alfvén waves

Abstract: Exact solitary Alfven waves are considered taking into account small, but finite β effects. The solitary waves consist of density humps whose amplitude has an upper limit.

Nonlinear Langmuir waves during type III solar radio bursts.

Abstract: Type III solar radio bursts are thought to be associated with intense levels of electron beam excited Langmuir waves. We numerically study the nonlinear evolution of these waves, in time and in two spatial dimensions, due to their coupling to other waves. For parameters appropriate to one-half the Earth-Sun distance, we find nonlinear effects to be important, as in previous one-dimensional work. However, a new and important phenomenon, two-dimensional soliton collapse, is found to occur. This collapse, induced directly by the wave packet nature of the beam excited waves, produces two-dimensional wave spectra extending over a much broader range of wavenumbers than has been predicted by inhomogeneous quasi-linear theory. Our results compare favorably with certain aspects of recent observations. We neglect the background magnetic field; while substantially justified for the present parameters, this neglect may require reexamination at locations closer to the Sun.

Excitation of instability waves in a two-dimensional shear layer by sound

Abstract: The excitation of instability waves in a plane compressible shear layer by sound waves is studied. The problem is formulated mathematically as an inhomogeneous boundary-value problem. A general solution for abitrary incident sound wave is found by first constructing the Green's function of the problem. Numerical values of the coupling constants between incident sound waves and excited instability waves for a range of flow Mach number are calculated. The effect of the angle of incidence in the case of a beam of acoustic waves is analyzed. It is found that for moderate subsonic Mach numbers a narrow beam aiming at an angle between 50 to 80 deg to the flow direction is most effective in exciting instability waves.

The Coupling of Alfven and Compressional Waves.

Abstract: The article studies the hydromagnetic wave propagation characteristics in a mixture of cold and hot plasma in the presence of an inhomogeneous magnetic field. Electron and ion distribution functions with a temperature anisotropy and a density gradient are used to obtain the dispersion equation by solving the Vlasov equation and Maxwell equations. From the solutions of the dispersion equation we find that the Alfven waves can couple to unstable drift mirror waves under certain conditions. The polarization of the coupled waves is studied for varying parameters of temperature anisotropy and the cold to hot density ratio. From detailed comparison of the theoretical results with the low-frequency wave properties observed in the magnetosphere we propose that the storm-associated magnetic field oscillations with periods of 100-600 s might be caused by the coupling of Alfven waves and the unstable drift mirror waves.

Scattering matrix for elastic waves. II. Application to elliptic cylinders

Abstract: Using the scattering‐matrix approach to elastic wave scattering, numerical results are presented for the scattering of P, SV, and SH waves from a cylinder of elliptic cross section for ratios of minor to major axis ranging from 0.25 to 1.0 and for nondimensional wave numbers in the range 0.1–3.2. Calculations were made for a tungsten cylinder embedded in aluminum and also for a cylindrical cavity in aluminum. The incident waves are taken to be plane waves incident obliquely with respect to the major axis of the ellipse.

Wave action and set-down for waves on a shear current

Abstract: This paper considers steady, slowly varying water waves propagating over a gently sloping bed on a steady current. The current varies linearly with depth, and so has constant vorticity ω. The analysis is two-dimensional and dissipation is neglected. Definitions, and expressions correct to second order in the amplitude, are given for the radiation stress, wave energy density E and total energy flux. An average La-grangian [Lscr ], obtained by heuristic arguments from Clebsch potentials, leads to the result that for this particular problem E equals the wave action [Lscr ]ω times the angular frequency ωrm relative to a frame of reference moving with the average-over-depth current velocity Um. This determines the variation of the amplitude with distance explicitly. An analytical expression for the height of the mean water surface is found by a heuristic argument which compares the conservation equations for total energy and wave action. All the results have been checked directly by substitution back into the basic equations. Graphs illustrate the effect of the vorticity ω on the wavelength, amplitude and set-down.

Three-dimensional lee-wave pattern

Abstract: Satellite photographs are analysed to study the lee-wave patterns generated by isolated islands in the Norwegian Sea and the Barents Sea. In situations where the wave motion is confined to the lower atmosphere (trapped waves) the waves are located within a wedge-shaped wake behind the islands. Both the diverging wave type, where the crests are orientated outwards from the centre of the wake, and the transverse wave type, where the crests are nearly perpendicular to the wind direction, are observed. The former wave type is, however, the more common. In certain situations a long single-crested wave is observed at Jan Mayen. The wave appears on photographs as a straight lane in the cloud layer. In one case it extends sideways from the island to a distance of about 350km. Wave kinematics is used to obtain the phase lines for a steady wave pattern for different atmospheric models. The theory is found to explain some important features of observed wave forms.

Acceleration waves and second sound in a perfect fluid

Abstract: The evolutionary behaviour of acceleration waves of arbitrary shape in a perfect fluid is investigated. The theory employed allows two coupled mechanical and temperature acceleration waves to propagate with finite wavespeeds. New results are described for waves entering isothermal regions but where the exterior flow velocity is non-zero.

Predictability of strong ground motion in the imperial valley: modeling the m4.9, november 4, 1976 brawley earthquake

Abstract: Strong-motion displacements, recorded at 33 km (IVC) and 36 km (ELC) from the November 4, 1976 Brawley earthquake, are modeled using the Cagniard-deHoop technique. The IVC record consists almost entirely of transversely polarized motion, whereas the ELC record contains an approximately equal proportion of transversely and radially polarized motion. A simplified shear-wave velocity model was determined from the compressional wave refraction studies of Biehler, Kovach, and Allen (1964). The epicentral location and focal mechanism computed from P-wave first-arrival studies were used to locate and orient a double-couple point source within the layered half-space. The far-field time function and source depth were the only parameters without good independent constraints. A triangular far-field time function with a duration of 1.5 sec and a source depth of 7 km were sufficient to model the first 25 sec of tangential ground motion. It appears that the effects of velocity structure on the propagation of long-period SH waves are predictable in the Imperial Valley. A study of the synthetic Fourier amplitude spectra indicates that wave propagation effects should be included in studies of source spectra and seismic wave attenuation.

Surface‐wave rays in elastodynamic diffraction by cracks

Abstract: A geometrical diffraction theory has been worked out to analyze the fields generated by diffraction of high‐frequency waves by cracks. The theory accounts for curvature of incident wavefronts, curvature of crack edges, and finite dimensions of the crack by providing first‐order corrections to the results for a semi‐infinite crack. The diffracted fields include direct diffractions from the crack edges as well as well as diffractions of signals which travel via the crack faces. On the faces of the crack the main contributions to the diffracted fields come from rays of surface waves. The directions of these surface‐wave rays, and the amplitudes, wavelengths, and phases of the associated surface‐wave motions have been related to the corresponding quantities of the incident body‐wave rays. Reflection and diffraction of surface‐wave rays by the edge of a crack have also been analyzed. As an example, diffraction by a penny‐shaped crack of a plane longitudinal wave under normal incidence has been considered in some detail. Explicit expressions are given for the diffracted fields. In these expressions a correction was introduced to extend the validity of the results to the normal axis through the center of the crack, which is a caustic axis. A simple expression for the scattering cross section is presented.

Piezoelectric acoustic boundary waves propagating along the interface between SiO 2 and LiTaO 3

Abstract: The propagation characteristics of the layered structure of thick Si02 film on 126° rotated Y-cut X-propagation LiTa03 are studied. The existence of the new piezoelectric acoustic boundary waves (Stoneley type waves) has been found. The waves are tightly bound to the thick Si02 film-LiTa03 substrate interface. Piezoelectric acoustic boundary waves appear beyond H/λ = 0.5, where H is the film thickness and λ is the acoustic boundary wave length. At H/λ = 1.0, the energy concentration coefficient, η = |Us|2 / l |Ui|2 is 0.08, where Us and Ui, are displacement at the surface and interface, respectively, and piezoelectric coupling coefficient K2 is 0.02. The experimental results agree with the calculated results.

Measurement of high frequency capillary waves on steep gravity waves

Abstract: The properties of high frequency capillary waves generated by steep gravity waves on deep water have been measured with a high resolution laser optical slope gauge. The results have been compared with the steady theory of Longuet-Higgins (1963). Good qualitative agreement is obtained. However, the quantitative predictions of the capillary wave slopes cannot be verified by the data because the theory requires knowledge of an idealized quantity - the crest curvature of the gravity wave in the absence of surface tension - which cannot be measured experimentally.