Showing papers on "Longitudinal wave published in 1985"

Relationships between compressional‐wave and shear‐wave velocities in clastic silicate rocks

Abstract: New velocity data in addition to literature data derived from sonic log, seismic, and laboratory measurements are analyzed for clastic silicate rocks. These data demonstrate simple systematic relationships between compressional and shear wave velocities. For water-saturated clastic silicate rocks, shear wave veloci­ ty is approximately linearly related to compressional wave velocity and the compressional-to-shear velocity ratio decreases with increasing compressional velocity. Laboratory data for dry sandstones indicate a nearly constant compressional-to-shear velocity ratio with rigidity approximately equal to bulk modulus. Ideal models for regular packings of spheres and cracked solids exhibit behavior similar to the observed water­ saturated and dry trends. For dry rigidity equal to dry bulk modulus, Gassmann's equations predict velocities in close agreement with data from the water-saturated

Plane waves in linear elastic materials with voids

Abstract: The behavior of plane harmonic waves in a linear elastic material with voids is analyzed. There are two dilational waves in this theory, one is predominantly the dilational wave of classical linear elasticity and the other is predominantly a wave carrying a change in the void volume fraction. Both waves are found to attenuate in their direction of propagation, to be dispersive and dissipative. At large frequencies the predominantly elastic wave propagates with the classical elastic dilational wave speed, but at low frequencies it propagates at a speed less than the classical speed. It makes a smooth but relatively distinct transition between these wave speeds in a relatively narrow range of frequency, the same range of frequency in which the specific loss has a relatively sharp peak. Dispersion curves and graphs of specific loss are given for four particular, but hypothetical, materials, corresponding to four cases of the solution.

Wave formation on a vertical falling liquid film

Abstract: The method of integral relations is used to derive a nonlinear two-wave equation for long waves on the surface of vertical falling liquid films. This equation is valid within a range of moderate Reynolds numbers and and be reduced in some cases to other well-known equations. The theoretical results for the fastest growing waves are compared with the experimental results concerning velocities, wave numbers, and growth rates of the waves in the inception region. The validity of the theoretical assumptions is also confirmed by direct measurements of instantaneous velocity profiles in a wave liquid film. The results of the experimental investigation concerning nonlinear stationary waves and the evolution of initial solitary disturbances are presented.

Mechanics of continua and wave dynamics

Abstract: I Theory of Elasticity.- 1. The Main Types of Strain in Elastic Solids.- 1.1 Equations of Linear Elasticity Theory.- 1.1.1 Hooke's Law.- 1.1.2 Differential Form of Hooke's Law. Principle of Superposition.- 1.2 Homogeneous Strains.- 1.2.1 An Elastic Body Under the Action of Hydrostatic Pressure.- 1.2.2 Longitudinal Strain with Lateral Displacements Forbidden.- 1.2.3 Pure Shear.- 1.3 Heterogeneous Strains.- 1.3.1 Torsion of a Rod.- 1.3.2 Bending of a Beam.- 1.3.3 Shape of a Beam Under Load.- 1.4 Exercises.- 2. Waves in Rods, Vibrations of Rods.- 2.1 Longitudinal Waves.- 2.1.1 Wave Equation.- 2.1.2 Harmonic Waves.- 2.2 Reflection of Longitudinal Waves.- 2.2.1 Boundary Conditions.- 2.2.2 Wave Reflection.- 2.3 Longitudinal Oscillations of Rods.- 2.4 Torsional Waves in a Rod. Torsional Vibrations.- 2.5 Bending Waves in Rods.- 2.5.1 The Equation for Bending Waves.- 2.5.2 Boundary Conditions. Harmonic Waves.- 2.5.3 Reflection of Waves. Bending Vibrations.- 2.6 Wave Dispersion and Group Velocity.- 2.6.1 Propagation of Nonharmonic Waves.- 2.6.2 Propagation of Narrow-Band Disturbances.- 2.7 Exercises.- 3. General Theory of Stress and Strain.- 3.1 Description of the State of a Deformed Solid.- 3.1.1 Stress Tensor.- 3.1.2 The Strain Tensor.- 3.1.3 The Physical Meaning of the Strain Tensor's Components.- 3.2 Equations of Motion for a Continuous Medium.- 3.2.1 Derivation of the Equation of Motion.- 3.2.2 Strain-Stress Relation. Elasticity Tensor.- 3.3 The Energy of a Deformed Body.- 3.3.1 The Energy Density.- 3.3.2 The Number of Independent Components of the Elasticity Tensor.- 3.4 The Elastic Behaviour of Isotropic Bodies.- 3.4.1 The Generalized Hooke's Law for an Isotropic Body.- 3.4.2 The Relationship Between Lame's Constants and E and v.- 3.4.3 The Equations of Motion for an Isotropic Medium.- 3.5 Exercises.- 4. Elastic Waves in Solids.- 4.1 Free Waves in a Homogeneous Isotropic Medium.- 4.1.1 Longitudinal and Transverse Waves.- 4.1.2 Boundary Conditions for Elastic Waves.- 4.2 Wave Reflection at a Stress-Free Boundary.- 4.2.1 Boundary Conditions.- 4.2.2 Reflection of a Horizontally Polarized Wave.- 4.2.3 The Reflection of Vertically Polarized Waves.- 4.2.4 Particular Cases of Reflection.- 4.2.5 Inhomogeneous Waves.- 4.3 Surface Waves.- 4.3.1 The Rayleigh Wave.- 4.3.2 The Surface Love Wave.- 4.3.3 Some Features of Love's Waves.- 4.4 Exercises.- 5. Waves in Plates.- 5.1 Classification of Waves.- 5.1.1 Dispersion Relations.- 5.1.2 Symmetric and Asymmetric Modes.- 5.1.3 Cut-Off Frequencies of the Modes.- 5.1.4 Some Special Cases.- 5.2 Normal Modes of the Lowest Order.- 5.2.1 Quasi-Rayleigh Waves at the Plate's Boundaries.- 5.2.2 The Young and Bending Waves.- 5.3 Equations Describing the Bending of a Thin Plate.- 5.3.1 Thin Plate Approximation.- 5.3.2 Sophie Germain Equation.- 5.3.3 Bending Waves in a Thin Plate.- 5.4 Exercises.- II Fluid Mechanics.- 6. Basic Laws of Ideal Fluid Dynamics.- 6.1 Kinematics of Fluids.- 6.1.1 Eulerian and Lagrangian Representations of Fluid Motion.- 6.1.2 Transition from One Representation to Another.- 6.1.3 Convected and Local Time Derivatives.- 6.2 System of Equations of Hydrodynamics.- 6.2.1 Equation of Continuity.- 6.2.2 The Euler Equation.- 6.2.3 Completeness of the System of Equations.- 6.3 The Statics of Fluids.- 6.3.1 Basic Equations.- 6.3.2 Hydrostatic Equilibrium. Vaisala Frequency.- 6.4 Bernoulli's Theorem and the Energy Conservation Law.- 6.4.1 Bernoulli's Theorem.- 6.4.2 Some Applications of Bernoulli's Theorem.- 6.4.3 The Bernoulli Theorem as a Consequence of the Energy-Conservation Law.- 6.4.4 Energy Conservation Law in the General Case of Unsteady Flow.- 6.5 Conservation of Momentum.- 6.5.1 The Specific Momentum Flux Tensor.- 6.5.2 Euler's Theorem.- 6.5.3 Some Applications of Euler's Theorem.- 6.6 Vortex Flows of Ideal Fluids.- 6.6.1 The Circulation of Velocity.- 6.6.2 Kelvin's Circulation Theorem.- 6.6.3 Helmholtz Theorems.- 6.7 Exercises.- 7. Potential Flow.- 7.1 Equations for a Potential Flow.- 7.1.1 Velocity Potential.- 7.1.2 Two-Dimensional Flow. Stream Function.- 7.2 Applications of Analytical Functions to Problems of Hydrodynamics.- 7.2.1 The Complex Flow Potential.- 7.2.2 Some Examples of Two-Dimensional Flows.- 7.2.3 Conformal Mapping.- 7.3 Steady Flow Around a Cylinder.- 7.3.1 Application of Conformal Mapping.- 7.3.2 The Pressure Coefficient.- 7.3.3 The Paradox of d'Alembert and Euler.- 7.3.4 The Flow Around a Cylinder with Circulation.- 7.4 Irrotational Flow Around a Sphere.- 7.4.1 The Flow Potential and the Particle Velocity.- 7.4.2 The Induced Mass.- 7.5 Exercises.- 8. Flows of Viscous Fluids.- 8.1 Equations of Flow of Viscous Fluid.- 8.1.1 Newtonian Viscosity and Viscous Stresses.- 8.1.2 The Navier-Stokes Equation.- 8.1.3 The Viscous Force.- 8.2 Some Examples of Viscous Fluid Flow.- 8.2.1 Couette Flow.- 8.2.2 Plane Poiseuille Flow.- 8.2.3 Poiseuille Flow in a Cylindrical Pipe.- 8.2.4 Viscous Fluid Flow Around a Sphere.- 8.2.5 Stokes' Formula for Drag.- 8.3 Boundary Layer.- 8.3.1 Viscous Waves.- 8.3.2 The Boundary Layer. Qualitative Considerations.- 8.3.3 Prandl's Equation for a Boundary Layer.- 8.3.4 Approximate Theory of a Boundary Layer in a Simple Case.- 8.4 Exercises.- 9. Elements of the Theory of Turbulence.- 9.1 Qualitative Considerations. Hydrodynamic Similarity.- 9.1.1 Transition from a Laminar to Turbulent Flow.- 9.1.2 Similar Flows.- 9.1.3 Dimensional Analysis and Similarity Principle.- 9.1.4 Flow Around a Cylinder at Different Re.- 9.2 Statistical Description of Turbulent Flows.- 9.2.1 Reynolds' Equation for Mean Flow.- 9.2.2 Turbulent Viscosity.- 9.2.3 Turbulent Boundary Layer.- 9.3 Locally Isotropic Turbulence.- 9.3.1 Properties of Developed Turbulence.- 9.3.2 Statistical Properties of Locally Isotropic Turbulence.- 9.3.3 Kolmogorov's Similarity Hypothesis.- 9.4 Exercises.- 10. Surface and Internal Waves in Fluids.- 10.1 Linear Equations for Waves in Stratified Fluids.- 10.1.1 Linearization of the Hydrodynamic Equations.- 10.1.2 Linear Boundary Conditions.- 10.1.3 Equations for an Incompressible Fluid.- 10.2 Surface Gravity Waves.- 10.2.1 Basic Equations.- 10.2.2 Harmonic Waves.- 10.2.3 Shallow- and Deep-Water Approximations.- 10.2.4 Wave Energy.- 10.3 Capillary Waves.- 10.3.1 "Pure" Capillary Waves.- 10.3.2 Gravity-Capillary Surface Waves.- 10.4 Internal Gravity Waves.- 10.4.1 Introductory Remarks.- 10.4.2 Basic Equation for Internal Waves. Boussinesq Approximation.- 10.4.3 Waves in an Unlimited Medium.- 10.5 Guided Propagation of Internal Waves.- 10.5.1 Qualitative Analysis of Guided Propagation.- 10.5.2 Simple Model of an Oceanic Waveguide.- 10.5.3 Surface Mode. "Rigid Cover" Condition.- 10.5.4 Internal Modes.- 10.6 Exercises.- 11. Waves in Rotating Fluids.- 11.1 Inertial (Gyroscopic) Waves.- 11.1.1 The Equation for Waves in a Homogeneous Rotating Fluid.- 11.1.2 Plane Harmonic Inertial Waves.- 11.1.3 Waves in a Fluid Layer. Application to Geophysics.- 11.2 Gyroscopic-Gravity Waves.- 11.2.1 General Equations. The Simplest Model of a Medium.- 11.2.2 Classification of Wave Modes.- 11.2.3 Gyroscopic-Gravity Waves in the Ocean.- 11.3 The Rossby Waves.- 11.3.1 The Tangent of ?-Plane Approximation.- 11.3.2 The Barotropic Rossby Waves.- 11.3.3 Joint Discussion of Stratification and the ?-Effect.- 11.3.4 The Rossby Waves in the Ocean.- 11.4 Exercises.- 12. Sound Waves.- 12.1 Plane Waves in Static Fluids.- 12.1.1 The System of Linear Acoustic Equations.- 12.1.2 Plane Waves.- 12.1.3 Generation of Plane Waves. Inhomogeneous Waves.- 12.1.4 Sound Energy.- 12.2 Sound Propagation in Inhomogeneous Media.- 12.2.1 Plane Wave Reflection at the Interface of Two Homogeneous Media.- 12.2.2 Some Special Cases. Complete Transparency and Total Reflection.- 12.2.3 Energy and Symmetry Considerations.- 12.2.4 A Slowly-Varying Medium. Geometrical-Acoustics Approximation.- 12.2.5 Acoustics Equations for Moving Media.- 12.2.6 Guided Propagation of Sound.- 12.3 Spherical Waves.- 12.3.1 Spherically-Symmetric Solution of the Wave Equation.- 12.3.2 Volume Velocity or the Strength of the Source. Reaction of the Medium.- 12.3.3 Acoustic Dipole.- 12.4 Exercises.- 13. Magnetohydrodynamics.- 13.1 Basic Concepts of Magnetohydrodynamics.- 13.1.1 Fundamental Equations.- 13.1.2 The Magnetic Pressure. Freezing of the Magnetic Field in a Fluid.- 13.1.3 The Poiseuille (Hartmann) Flow.- 13.2 Magnetohydrodynamic Waves.- 13.2.1 Alfven Waves.- 13.2.2 Magnetoacoustic Waves.- 13.2.3 Fast and Slow Magnetoacoustical Waves.- 13.3 Exercises.- 14. Nonlinear Effects in Wave Propagation.- 14.1 One-Dimensional Nonlinear Waves.- 14.1.1 The Nonlinearity Parameter.- 14.1.2 Model Equation. Generation of Second Harmonics.- 14.1.3 The Riemann Solution. Shock Waves.- 14.1.4 Dispersive Media. Solitons.- 14.2 Resonance Wave Interaction.- 14.2.1 Conditions of Synchronism.- 14.2.2 The Method of Slowly-Varying Amplitudes.- 14.2.3 Multiwave Interaction.- 14.2.4 Nonlinear Dispersion.- 14.3 Exercises.- Appendix: Tensors.- Bibliographical Sketch.

Radiation from a point source and scattering theory in a fluid-saturated porous solid

Abstract: The time harmonic Green function for a point load in an unbounded fluid‐saturated porous solid is derived in the context of Biot’s theory. The solution contains the two compressional waves and one transverse wave that are predicted by the theory and have been observed in experiments. At low frequency, the slow compressional wave is diffusive and only the fast compressional and transverse waves radiate energy. At high frequency, the slow wave radiates, but with a decay radius which is on the order of cm in rocks. The general problem of scattering by an obstacle is considered. The point load solution may be used to obtain scattered fields in terms of the fields on the obstacle. Explicit expressions are presented for the scattering amplitudes of the three waves. Simple reciprocity relations between the scattering amplitudes for plane‐wave incidence are also given. These hold under the interchange of incident and observation directions and are completely general results. Finally, the point source solution is Fourier transformed to get the solution for a load which is a delta function in time as well as space. We obtain a closed form expression when there is no damping. The three waves radiate from the source as distinct delta function pulses. With damping present, asymptotic approximations show the slow wave to be purely diffusive. The fast and transverse waves propagate as pulses. The pulses are Gaussian‐shaped, which broaden with increasing time or radial distance.

Azimuthal propagation and frequency characteristic of compressional Pc 5 waves observed at geostationary orbit

Abstract: Energetic particle data from the 1977-007 and 1979-053 satellites and magnetic field data from the GOES 2 and 3 satellites have been used to study eight compressional Pc 5 wave events observed at geostationary orbit during 1979. All the events occurred on the dayside, and most of them were observed during the recovery phase of a geomagnetic storm. By using the data from two of the satellites which were close to each other, we measured the azimuthal phase velocity V/sub phi/ and azimuthal wave number m for selected intervals. For all these intervals the waves propagated westward in the spacecraft frame, and we obtained Vertical Bar V/sub phi/ Vertical Bar = 4--14 km/s and Vertical Bar m Vertical Bar = 40--120. In addition, harmonics of a local standing Alfven wave were often present simultaneously with a compressional Pc 5 wave. The frequency of the compressional wave was typically 25% of that of the second harmonic of the Alfven wave. These observed features are discussed in the light of existing theories of instabilities in the ring current plasma.

Steady Deep‐Water Waves on a Linear Shear Current

Abstract: The behavior of steady, periodic, deep-water gravity waves on a linear shear current is investigated. A weakly nonlinear approximation for the small amplitude waves is constructed via a variational principle. A local analysis of those large amplitude waves with sharp crests, called extreme waves, is also provided. To construct solutions for all waveheights (especially the limiting ones) a convenient mathematical formulation which involves only the wave profile and some constants of the motion is derived and then solved by numerical means. It is found that for some shear currents the highest waves are not necessarily the extreme waves. Furthermore a certain non-uniqueness in the sense of a fold is shown to exist and a new type of limiting wave is discovered.

Ion‐acoustic solitary waves in relativistic plasmas

Abstract: This is a sequel to our earlier study on ion‐acoustic waves studied through the augmentation to a modified Korteweg–deVries (K–dV) equation. We have derived a K–dV equation in a plasma, taking account of weakly relativistic effects, and the result shows that the solitary wave does exhibit the relativistic effect in the presence of ion streaming.

Nonlinear electromagnetic waves guided by a single interface

Abstract: Electromagnetic waves guided by the interface between two nonlinear media, and a nonlinear and a linear medium are investigated theoretically and numerically. Both s‐ and p‐polarized waves are analyzed and the guided wave power versus guided wave vector is evaluated for a variety of material conditions. The consequences of two different versions of the uniaxial approximation for the p‐polarized case are compared. The power‐dependent attenuation is approximately evaluated.

Surface Acoustic Waves

Abstract: In 1887 Lord Rayleigh(1) showed that a semi-infinite, isotropic, elastic medium, bounded by a single, stress-free, planar surface, can support surface vibration modes that are wavelike in directions parallel to the surface of the solid, but whose amplitudes decay exponentially with increasing distance into the solid from the surface, with a decay length that is of the order of the wavelength of the wave along the surface. The displacement vector of these waves lies in the sagittal plane, i.e. in the plane defined by the direction of propagation of the wave and the normal to the surface. These waves are acoustic waves in that their frequencies are linear in the magnitude of the two-dimensional wave vector characterizing their propagation along the surface. They are consequently non dispersive, i.e. their speed of propagation is independent of their wavelength parallel to the surface, which is due to the absence of a characteristic length in the system under consideration. Their frequencies also lie below the continuum of frequencies allowed the normal vibration modes of an infinite elastic medium for the same value of the two-dimensional wave vector. Such surface acoustic waves are now known as Rayleigh Waves.

An Analytical Model of Periodic Waves in Shallow Water

Abstract: : An explicit, analytical model is presented of finite amplitude waves in shallow water. The waves in question have two independent spatial periods, in two independent horizontal directions. Both short-crested and long-crested waves are available from the model. Every wave pattern is an exact solution of the Kadomtsev-Petviashvili equation, and is based on a Riemann theta function of genus 2. These bi-periodic waves are direct generalizations of the well-known (simply periodic) cnoidal waves. Just as cnoidal waves are often used as one-dimensional models of typical nonlinear, periodic waves in shallow water, these bi-periodic waves may be considered to represent typical nonlinear, periodic waves in shallow water without the assumption of one-dimensionality. (Author)

Method of making a piezoelectric shear wave resonator

Abstract: An acoustic shear wave resonator comprising a piezoelectric film having its C-axis substantially inclined from the film normal such that the shear wave coupling coefficient significantly exceeds the longitudinal wave coupling coefficient, whereby the film is capable of shear wave resonance, and means for exciting said film to resonate. The film is prepared by deposition in a dc planar magnetron sputtering system to which a supplemental electric field is applied. The resonator structure may also include a semiconductor material having a positive temperature coefficient of resonance such that the resonator has a temperature coefficient of resonance approaching 0 ppm/°C.

Seismic anisotropy in the upper oceanic crust

Abstract: Seismic anisotropy in the upper oceanic crust is observed in borehole data obtained at Deep Sea Drilling Project (DSDP) site 504B on DSDP leg 92. Particle motion analysis of converted shear wave arrivals from explosive sources at various azimuths reveals a set of patterns which is indicative of hexagonally isotropic structure with a horizontal symmetry axis. There are four diagnostic patterns: (1) Along symmetry axes, where vertically polarized shear waves (SV) are generated but horizontally polarized shear waves (SH) are not generated, the particle motions are purely vertical, (2) for azimuths at which both SV and SH are generated and the SH velocity is significantly faster than SV, a cruciform pattern with horizontal first motion is observed, (3) for azimuths at which both are generated and the SV velocity is significantly faster than SH, a cruciform pattern with vertical first motion is observed, and (4) for azimuths at which both are generated and SV and SH velocities are similar elliptical particle motions are observed. The shear wave particle motions and compressional wave travel times (from a 2-km radius circle) are consistent with an anisotropic model with hexagonal symmetry. The compressional wave velocity has a two theta azimuthal variation between 4.0 and 5.0 km/s. The symmetry axis is horizontal with an azimuth of N20°W±10°. The spreading direction at the site (6 m.y. age) is north-south. The observed seismic anisotropy is most probably caused by the preferred orientation of large-scale fractures and fissures in upper layer 2 which were created in the early stages of crustal development by near axis extensional processes and normal block faulting.

The fourth-order evolution equation for deep-water gravity-capillary waves

Abstract: The stability of a train of nonlinear gravity-capillary waves on the surface of an ideal fluid of infinite depth is considered. An evolution equation is derived for the wave envelope, which is correct to fourth order in the wave steepness. The derivation is made from the Zakharov equation under the assumption of a narrow band of waves, and including the full form of the interaction coefficient for gravity-capillary waves. It is assumed that conditions are away from subharmonic resonant wavelengths. Just as was found by K. B. Dysthe ( Proc. R. Soc. Lond . A 369 (1979)) for pure gravity waves, the main difference from the third-order evolution equation is, as far as stability is concerned, the introduction of a mean flow response. There is a band of waves that remains stable to fourth order. In general the mean flow effects for pure capillary waves are of opposite sign to those of pure gravity waves. The second-order corrections to first-order stability properties are shown to depend on the interaction between the mean flow and the envelope frequency-dispersion term in the governing equation. The results are shown to be in agreement with some recent computations of the full problem for sufficiently small values of the wave steepness.

Scattering by a spherical inhomogeneity in a fluid‐saturated porous medium

Abstract: A fast compressional wave incident on an inhomogeneity in a fluid‐saturated porous medium will produce three scattered elastic waves: a fast compressional wave, a slow compressional wave, and a shear wave. This problem is formulated as a multipole expansion using Biot’s equations of poroelasticity. The solution for the first term (n=0) in the multipole series involves a 4×4 system which is solved analytically in the long‐wavelength limit. All higher‐order terms (n≥1) require the solution of a 6×6 system. A procedure for solving these equations by splitting the problem into a 4×4 system and a 2×2 system and then iterating is introduced. The first iterate is just the solution of the elastic wave scattering problem in the absence of fluid effects. Higher iterates include the successive perturbation effects of fluid/solid interaction.

Nonlinear evolution of slow waves in the solar wind.

Abstract: It is shown by numerical simulation using a hybrid code that comparison of the nonlinear steepening rate, calculated from fluid theory, with the linear collisionless damping rate defines reasonably well the parameters for which fast and slow MHD waves should steepen. The results indicate that, whereas fast modes should ordinarly steepen, steepened slow waves should occur rarely in the solar wind near 1 AU.

Experiments on the generation of internal waves in a stratified fluid

Abstract: This paper presents an overview of the results of an experimental study of internal gravity waves produced as a result of the motion of a self-propelled vehicle through a fluid in which the density varies with depth. Two ambient density profiles are considered: one for which the characteristic vertical length scale of the density change is large compared to the vehicle diameter, and a second in which this scale is smaller than the diameter. The most significant results show a strong coupling between wake turbulence and short, random internal waves. In the presence of sharp density gradients, the experiments reveal the onset of nonlinear influences on propagation, leading to the formation of solitary waves. Comparisons with theory are also presented.

Are observed broadband plasma wave amplitudes large enough to explain the enhanced electron temperatures of the high-latitude E region?

Abstract: We have studied the possibility that the electron heating that has been observed in the high-latitude E region during disturbed periods is produced by low-frequency broadband waves of the type that is measured on rockets. We have found that low-frequency waves can be responsible for the observed electron temperature enhancements if a significant portion of the large amplitude waves does not have a wave vector exactly perpendicular to the magnetic field, but rather if their wavevector is a few (2--5) degrees away from perpendicularity. We show that this aspect angle constraint is present because in order to heat the electrons efficiently with low-frequency waves in the magnetized E region we need a large enough component of the perturbed electric field in the magnetic field direction. While aspect angles that are larger than expected from classical linear theory have been detected at times, we propose that they should be limited to low-frequency gradient drift waves. For such waves nonlocal effects are probably strong enough to force the waves to be less field aligned than originally expected. Finally a direct implication of our findings is that a heating mechanism similar to the one discussed in the present paper may produce detectable effectsmore » in the equatorial E region during strong electrojet conditions.« less

Charged particle behavior in low‐frequency geomagnetic pulsations: 4. Compressional waves

Abstract: In this fourth paper of a series concerning charged particle behavior in ultralow frequency waves in the terrestrial magnetosphere, we examine the particle flux response expected in waves with a strong compressional magnetic component. Two effects, which we label betatron and mirror, dominate the behavior expected for nonresonant particles with the mirror effect expected in most circumstances. Resonant behavior is a strong function of signal symmetry, much as discussed in earlier papers. We conclude by examining recently published observations of particle flux oscillations associated with compressional signals.

The scattering of ultrasonic waves in polycrystalline materials with texture

Abstract: The theory of ultrasonic propagation in polycrystals with independent and uniformly distributed orientations of the grains presented in previous papers [J. Acoust. Soc. Am. 72, 1021–1031 (1982); 73, 1160–1163 (1983)] is generalized to calculate the scattering coefficients and the phase and group velocities of plane compressional and shear waves in textured polycrystals. The calculation was done for plane waves in polycrystals of cubic symmetry with rolling texture in second‐order perturbation theory using the assumption that the changes in the material constants from grain to grain are small. In the limit texture equal to zero the analytical results are exactly the same as those for untextured polycrystals previously presented. Numerical calculations are carried out for some examples.

Broadband electrostatic noise produced by ion beams in the Earth's magnetotail

Abstract: Spacecraft observations in the earth's magnetotail at distances of 30 to 40 R(E) have revealed the presence of broadband electrostatic waves These waves are generally most intense in the regions just outside of the plasma sheet and are correlated with the observations of relatively cold and energetic ion beams traveling in either the earthward or the tailward direction These waves are observed to propagate obliquely to the geomagnetic field with wave normal angles around 70 deg Because the broadband electrostatic noise is the most intense of the waves observed in the magnetotail, it is important to understand the generation mechanism of these waves The purpose of this study is to provide for the first time a correct solution to the dispersion equation for ion beams observed in the magnetotail By numerically solving this equation, it is shown that obliquely propagating waves have growth rates that can be an order of magnitude larger than those of parallel propagating waves, in agreement with observations In addition, the effect of beam temperature on the ion beam instability is studied, and it is shown that this instability can be a viable generation mechanism only when the ion beam has a relatively small thermal spread

Sensitivity to shearing and compressive motion in random dots.

Abstract: The sensitivity of the visual system to motion of differentially moving random dots was measured. Two kinds of one-dimensional motion were compared: standing-wave patterns where dot movement amplitude varied as a sinusoidal function of position along the axis of dot movement (longitudinal or compressional waves) and patterns of motion where dot movement amplitude varied as a sinusoidal function orthogonal to the axis of motion (transverse or shearing waves). Spatial frequency, temporal frequency, and orientation of the motion were varied. The major finding was a much larger threshold rise for shear than for compression when motion spatial frequency increased beyond 1 cycle deg-1. Control experiments ruled out the extraneous cues of local luminance or local dot density. No conspicuous low spatial-frequency rise in thresholds for any type of differential motion was seen at the lowest spatial frequencies tested, and no difference was seen between horizontal and vertical motion. The results suggest that at the motion threshold spatial integration is greatest in a direction orthogonal to the direction of motion, a view consistent with elongated receptive fields most sensitive to motion orthogonal to their major axis.

Detection of open fractures with vertical seismic profiling

Abstract: In vertical seismic profiling surveys, tube waves are generated by compressional waves impinging on subsurface fractures or permeable zones. The problem of generation of these waves by a nonnormal incident P wave for an inclined borehole intersecting a tilted parallel-wall fracture is formulated theoretically. The amplitude of tube waves depends on the permeability, the length of the fracture, and the frequency. The relative effects of these parameters are studied individually. The problem is also formulated for a thin oblate ellipsoidal (penny-shaped) fracture. The results for the two fracture models are compared and contrasted. Field data from Tyngsboro, Massachusetts, are shown for open fractures in granite. From tube wave amplitudes normalized to P wave amplitudes, calculated permeabilities are of the order of 100 mdarcy.

Generalized thermoelastic waves in transversely isotropic media

Abstract: In this paper the propagation of generalized thermoelastic waves in transversely isotropic media has been investigated. The basic equations have been solved by a general method after decoupling the SH wave, which is not affected by thermal variations and is independent of the rest of the motion. The discussion of the frequency equation reveals that in general there are three distinct waves in transversely isotropic media. The particle paths during the motion are found to be elliptic. The inclinations of the major axes with wave normal and the eccentricities of elliptical paths have been determined. The results have been verified numerically and are represented graphically for a single crystal of zinc in the case of waves of assigned frequency.

Interaction of Random Waves and Currents

Abstract: The effects of steady, uniform currents on random waves, and the associated waterparticle kinematics, are investigated. The basic equations describing the interactions between waves and currents ar...

General p, type-i s, and type-ii s waves in anelastic solids; inhomogeneous wave fields in low-loss solids.

Abstract: The physical characteristics for general plane-wave radiation fields in an arbitrary linear viscoelastic solid are derived. Expressions for the characteristics of inhomogeneous wave fields, derived in terms of those for homogeneous fields, are utilized to specify the characteristics and a set of reference curves for general P and S wave fields in arbitrary viscoelastic solids as a function of wave inhomogeneity and intrinsic material absorption. The expressions show that an increase in inhomogeneity of the wave fields causes the velocity to decrease, the fractional-energy loss ( Q −1 ) to increase, the deviation of maximum energy flow with respect to phase propagation to increase, and the elliptical particle motions for P and type-I S waves to approach circularity. Q −1 for inhomogeneous type-I S waves is shown to be greater than that for type-II S waves, with the deviation first increasing then decreasing with inhomogeneity. The mean energy densities (kinetic, potential, and total), the mean rate of energy dissipation, the mean energy flux, and Q −1 for inhomogeneous waves are shown to be greater than corresponding characteristics for homogeneous waves, with the deviations increasing as the inhomogeneity is increased for waves of fixed maximum displacement amplitude. For inhomogeneous wave fields in low-loss solids, only the tilt of the particle motion ellipse for P and type-I S waves is independent to first order of the degree of inhomogeneity. Quantitative estimates for the characteristics of inhomogeneous plane body waves in layered low-loss solids are derived and guidelines established for estimating the effect of inhomogeneity on seismic body waves and a Rayleigh-type surface wave in low-loss media.

Statistical characteristics of Pc5 waves at geostationary orbit.

Abstract: Statistical analyses were made to clarify the latitude dependence of occurrence and other characteristics of Pc5 waves near L=6.6, using magnetic field data obtained with GOES 2 and 3 during 1978-1984. It is found that the occurrence probability of Pc5 waves with azimuthal polarization (A-class) is small at GOES 3 (4.7°N in magnetic latitude), as compared with that at GOES 2 (9.3-11.4°N). Most of A-class waves observed at GOES 2 are simultaneously detected near the subsatellite point of GOES 2. A typical amplitude ratio of ground Pc5 pulsations to A-class Pc5 waves at synchronous orbit is about 5 (50nT/10nT). In contrast to the A-class waves, compressional waves with radial polarization, observed mostly in the afternoon around 15h LT during magnetically disturbed conditions, have a larger occurrence probability at GOES 3 than at GOES 2. Amplitudes of the compressional Pc5 are larger at GOES 3 than at GOES 2, when the wave simultaneously occurs at both the satellites. The difference of Pc5 characteristics at GOES 2 and 3 suggests that the compressional Pc5 wave is confined to a latitudinally narrow region near the magnetic equator. The compressional Pc5 can be further divided into two types. One is of long duration and mostly occurs around noon in the recovery phase of magnetic storm. The other is of short duration and is observed on the afternoon-dusk side. The occurrence of short-duration events is well correlated with the individual substorm onset. A systematic delay of Pc5 occurrence behind the substorm onset is statistically obtained as a function of the local time of the satellite position. This delay suggests that the source region of the short-duration compressional Pc5 drifts westward with a speed of the gradient drift of 50-60keV protons.

A note on the momentum transfer from wind to waves

Abstract: Momentum balance in the air-sea boundary process is discussed on the basis of a recent study (Mitsuyasu and Honda, 1982). It is shown that the momentum transferred from wind to water surface goes largely into water waves when the steepness of the waves is large. For wind-generated waves, however, much of the momentum transferred from wind to waves is lost by wave breaking, and only a small amount is advected by the wind waves.