Terms Of Surface Waves Research Articles

Primary breakup of liquid jet—Effect of jet velocity profile

The present work examines the effect of the velocity profile on primary breakup of liquid jets emanating from fuel injectors. Direct numerical simulation is used to simulate liquid jet breakup. Different velocity profiles are imposed on the liquid and their effect on breakup is examined. It is a common practice in the literature to use flat or uniform velocity profiles in such studies. The validity of this assumption is assessed and its implications are highlighted. Droplet sizes and degree of atomization are compared for all the cases. Further, a detailed comparison of jet breakup structure is made for two cases—parabolic and power-law velocity profiles. The liquid surface is observed to show two-dimensional waves initially, which subsequently transform into three-dimensional waves and give rise to ligament formation and surface breakup. Tip vortex rollup and its role in jet breakup is discussed. The distinction between different velocity profiles is examined in detail in terms of surface waves, degree of atomization, and jet structure.

Rayleigh-wave H/V ratio measurement from ambient noise cross-correlations and its sensitivity to VP: a numerical study

SUMMARY The promise of passive seismology has increasingly been realized in recent years. Given the expense in installing and maintaining seismic station networks, it is important to extract as much information from the measurements as possible. In this context, the ellipticity or H/V amplitude ratio of Rayleigh waves can prove to be a valuable observable in ambient noise seismology due to its complimentary sensitivity to subsurface structure, compared to phase and group-velocity dispersion, as well as its potential for constraining VP structure in addition to VS. However, the suitability of the Rayleigh H/V ratio in noise-based studies depends on the accurate interpretation of measurements made on multicomponent ambient-noise cross-correlations. We present a synthetic study that critically examines measurements commonly interpreted as the Rayleigh-wave H/V ratio, under realistic scenarios of spatially distributed and non-uniform noise sources. Using the surface wave terms of Green’s function in a laterally homogeneous medium, we rigorously model multicomponent cross-correlations for arbitrary noise-source distributions and extract from them standard estimates of the H/V ratio. Variation of these measurements as a function of VP is studied empirically, by brute-force simulation. We find that the measurements depart significantly from the theoretical Rayleigh-wave H/V for the medium in question, when noise sources are strongly directional or anisotropic. Love waves, if present in the cross-correlations, also have the potential to significantly bias interpretation. Accurate interpretation of the H/V ratio measurement thus rests on carefully modelling these effects. However, the sensitivity to VP structure is comparable to that of the classic Rayleigh-wave H/V. We also propose a new measurement for cross-correlations that has slightly greater sensitivity to VP. Finally, uncertainty analysis on synthetic tests suggests that simplistic interpretations of Rayleigh-wave ellipticity are only effective (in resolving VP structure) when the Love-wave contamination is negligible and measurement uncertainties are less than 10 per cent.

Study of Extraordinary Transmission in a Circular Waveguide System

Extraordinary transmission through periodic distributions of sub-wavelength holes made in opaque screens has been demonstrated and exhaustively studied along the last decade. More recently, extraordinary transmission has also been predicted and experimentally observed through electrically small diaphragms located inside hollow pipe waveguides. This last phenomenon cannot be explained in terms of surface waves excited along the periodic system (the so-called surface plasmon polaritons). Transverse resonances can be invoked, however, as a sound explanation for extraordinary transmission in this kind of systems. In this paper, a simple waveguide system, exhibiting exactly the same behavior previously observed in periodic 2-D arrays of holes, is analyzed in depth. Analogies and differences with the periodic case are discussed. The theoretical and experimental results reported in this paper provide strong evidence in favor of the point of view emphasizing the concept of impedance matching versus surface wave excitation. The role of material losses is discussed as an important practical issue limiting the maximum achievable subwavelength transmission level. Most of our conclusions can be applied to both periodic arrays of holes and diaphragms in closed waveguides.

A direct discrete complex image method from the closed-form Green's functions in multilayered media

Sommerfeld integration is introduced to calculate the spatial-domain Green's functions (GF) for the method of moments in multilayered media. To avoid time-consuming numerical integration, the discrete complex image method (DCIM) was introduced by approximating the spectral-domain GF by a sum of exponentials. However, traditional DCIM is not accurate in the far- and/or near-field region. Quasi-static and surface-wave terms need to be extracted before the approximation and it is complicated to extract the surface-wave terms. In this paper, some features of the matrix pencil method (MPM) are clarified. A new direct DCIM without any quasi-static and surface-wave extraction is introduced. Instead of avoiding large variations of the spectral kernel, we introduce a novel path to include more variation before we apply the MPM. The spatial-domain GF obtained by the new DCIM is accurate both in the near- and far-field regions. The CPU time used to perform the new DCIM is less than 1 s for computing the fields with a horizontal source-field separation from 1.6/spl times/10/sup -4//spl lambda/ to 16/spl lambda/. The new DCIM can be even accurate up to 160/spl lambda/ provided the variation of the spectral kernel is large enough and we have accounted for a sufficient number of complex images.

Analysis of Lightning-Radiated Electromagnetic Fields in the Vicinity of Lossy Ground

An antenna theory (AT) approach in the frequency domain is presented to compute electromagnetic fields radiated by a lightning return stroke. The lightning channel is modeled as a lossy-wire monopole antenna (a wire antenna with distributed resistance) energized by a current source at its base, and the ground is modeled as a lossy half-space. The method of moments is used for solving the governing electric field integral equation (EFIE) in the frequency domain. The resultant current distribution along the channel is used to calculate electromagnetic fields at different distances from the channel. All field components are evaluated using a rapid but accurate procedure based on a new approximation of Sommerfeld integrals. In contrast with the previous models, the approach proposed here is characterized by a self-consistent treatment of different field components in air or on the surface of a lossy half-space. It is shown that the omission of surface wave terms in the general field equations, as done in the perfect-ground approximation, can strongly affect model-predicted field components.

Some Observations About the Near Zone Electric Field of a Hertzian Dipole Above a Lossy Earth

In some recent publications, King (1990, 1992) and King and Sandler (1994) have provided formulas for the electromagnetic field radiated by an infinitesimal vertical Hertzian dipole above a lossy homogeneous half space (earth) and above a lossy half space coated by a thin dielectric layer. Several authors have questioned the accuracy of the King-Sandler formulas, particularly for field points close to the dipole (Yokoyama (1995), Wait (1996), Mahmoud (1999)). The authors have responded to these critiques by asserting that their formulas are accurate subject only to the restriction that the magnitude of the relative permittivity of the lossy half space is greater than 9. The principal results they obtain are that the near zone fields are independent of the electrical parameters of either the coating or the homogeneous half space. In this communication we provide some results obtained from a numerical evaluation of the exact integral for the near zone axial electric field along with numerical results obtained from an evaluation of the approximate integral used by King and Sandler. The King-Sandler formulas show that there is no contribution to the near zone axial electric field from a term they called the surface wave field. Our numerical evaluations show that this is not the case, in actual fact the surface wave term makes a significant contribution to the near zone axial electric field. We also present a quasistatic analysis that provides an alternative formula for calculating the near zone field. Our analysis supports the conclusions reached by Wait and Mahmoud.

An analytical method to estimate shadow and source overprint effects in CSAMT sounding

The controlled-source audio frequency magnetotelluric (CSAMT) method is well established in geophysical prospecting. By using a transmitter (usually a grounded electric dipole) to generate the source fields, the CSAMT method overcomes problems associated with weak natural EM fields used in conventional audio MT surveys. But the CSAMT method creates a new problem associated with active EM surveys: when anomalies are located between the transmitter and receiver, the measured data may be distorted so that the geological structure will be inferred incorrectly. Kuznetzov (1982) and Zonge and Hughes (1988) observe this phenomenon in 2D numerical model studies and term such behavior the shadow effect. This phenomenon has been simulated by numerical modeling and discussed in many papers (Newman et al., 1986; Zonge et al., 1986; Mitsuhata, 2000). Boschetto and Hohmann (1991) use numerical methods to study shadow and source overprint effects in CSAMT using a horizontal electric dipole source. For this problem, we separate the ground-wave and surface-wave terms from the closed-form expressions of the electric and magnetic fields in a uniform earth and use the ground-wave/surface-wave ratio to estimate the potential magnitude for producing shadow and source overprint effects. This is a new and effective analytical method.

Transients at the dusk side magnetospheric boundary: Surface waves or isolated plasma blobs?

We revisit Interball‐Tail and Magion‐4 observations of the dusk side magnetospheric boundary on February 15–16, 1996. The observed transient behavior of the boundary can be interpreted in terms of surface waves or as the manifestation of isolated magnetosheath plasma entities embedded in the magnetosphere. We examine the arguments for each of these interpretations with high time resolution magnetic field and plasma data and by exploiting the dual‐satellite nature of the observations. We find strong evidence for magnetic field and flow vortices near the magnetospheric boundary and hence for the existence of flux tubes with helicoidal field lines; such structures can be associated with both interpretations. The cross‐correlation between the dual satellite observations and the apparent periodicity strongly suggest a Kelvin‐Helmholtz surface wave, although other interpretations are not impossible. In any case, the observations for this particular event allow us to derive constraints on surface wave generation mechanisms and on scenarios that could account for the presence of isolated plasma elements in the magnetosphere.

Propagation of sound above an impedance plane in a downward refracting atmosphere

An asymptotic analysis has been carried out to study the propagation of sound at long ranges in an arbitrary downward refracting sound‐speed profile. It has been shown that the solution can be expressed in a form of the Weyl–Van der Pol formula and the present theory offers an extension for the established theory to the case of a vertically stratified medium. The analysis starts from the full wave equation and the derivation assumes that the ambient properties only depend on the height above an impedance ground and that there is no wind or turbulence in the medium. In addition, the theory also assumes that the sound speed of the atmosphere increases monotonically with height. For such an atmospheric condition, the medium forms a waveguide that enhances the sound levels at long ranges along the ground surface. It is demonstrated that the acoustical path length derived by the asymptotic method is identical to that derived by the analytical ray trace model. Furthermore, the asymptotic method also allows a proper inclusion of the surface wave term rigorously.

Anomalous mutual coupling between microstrip antennas

An asymptotic expansion of the microstrip Green's function is used to facilitate a study of mutual coupling between two printed antennas, and coupling versus element separation is presented for substrate parameters of practical interest. For certain substrate parameters, it is found that the magnitude of mutual coupling does not decay monotonically with increasing element separation. Instead, the magnitude exhibits a quasi-periodic oscillation which can be attributed to the interference of surface and space waves. The presentation and discussion of this anomalous behavior is the purpose of the paper. The asymptotic representation of the Green's function, which differentiates space wave terms from surface wave terms when source and observation points are largely separated, is used to characterize the behavior of mutual coupling in the principal planes.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

High-frequency scattering from a wedge with impedance faces illuminated by a line source. II. Surface waves

For pt.I see ibid., vol.37, no.2, p.212-18 (1989). In Part I a rigorous integral representation for the field scattered at a finite distance from the edge of an impedance wedge when it is illuminated by a line source was derived. It was shown that the total field can be expressed as the sum of the geometrical optics (GO) field, the field diffracted by the edge, and terms related to the excitation of surface waves. The double spectral integral representation for the diffracted field was asymptotically evaluated there, in the case in which no surface wave can be supported by the two faces of the wedge. In particular, the high-frequency solution was expressed in the special format of the uniform geometrical theory of diffraction (UTD). Here, field contributions related to the surface wave excitation mechanism are examined. By a convenient asymptotic approximation of the integrals, a high-frequency solution which is uniform with respect to aspects of both incidence and observation is obtained. Moreover, this solution has useful symmetry properties so that it explicitly exhibits reciprocity. Numerical results are presented to show the relevance of the surface wave terms in the evaluation of the field. >

One-station estimates of seismic moments from the mantle magnitudeM m: The case of the regional field (1.5�???15�)

We extend to the regional field of distances the procedure of one-station estimation of seismic moments using the mantle magnitudeMm, as introduced earlier in the case of teleseismic events. A theoretical analysis of the validity of the asymptotic expansion of normal modes in terms of surface waves, which was used in the development ofMm, upholds the validity of the algorithm for distances as short as 1.5°. This is confirmed by the analysis of a dataset of 149 GEOSCOPE records obtained at distances ranging from 1.5 to 15°, from earthquakes with moments between 1024 and 2.5×1027 dyn-cm. The performance ofMm as measured in terms of average residual with respect to published values ofM0, and standard deviation of the residuals, is not degraded in this distance range, with respect to the teleseismic case. This indicates that the mantle magnitudeMmcan be reliably used at regional distances, notably for tsunami warning applications.

Experimental study of the scattering of a compressional wave by an elastic wedge

We investigated the diffraction pattern of an acoustic beam produced by the edge of a dihedral angle. The incident beam is perpendicular to the edge, and the angular variations of the scattered field are recorded in a plane which is perpendicular to the edge. The frequency of excitation is 2.5 MHz, and the dimensions of the samples are much larger than the incident wavelength. The experimental measurements of the angular diagrams are discussed in terms of surface waves and conversion modes.

Computational study and complex angular momentum analysis of elastic scattering for complex optical potentials

A systematic study of elastic scattering by complex valued optical potentials has been carried out. A Lennard-Jones (12,6) potential with an imaginary r−s term has been used in the calculations. The collision parameters are chosen to model the elastic scattering of K by HBr and Li by HBr. First-order semiclassical single turning point phase shifts are compared with accurate quantum phase shifts and close agreement is found. It is straightforward to calculate semiclassical phase shifts for an optical potential; it is unnecessary to introduce additional approximations (for numerical convenience) as is usually done in the literature. Up to 15 000 terms in the partial wave series are used to calculate elastic angular distributions. It is shown that a rich interference structure and a backward glory can occur in the large angle scattering, provided the transition from absorbency to transparency is sufficiently rapid. Different optical potentials can result in similar angular distributions. A complex angular momentum (Regge pole) analysis of the large angle scattering has been carried out. It is shown that the interference effects have a physical interpretation in terms of surface waves that propagate around the core of the potential and the directly reflected elastic scattering.

The eigenfrequencies of spheroids obtained from an integral phase matching condition

The complex acoustic eigenfrequencies of impenetrable spheroids have been found previously by satisfying the boundary conditions with spheroidal wavefunctions [$. M. D'Archangelo et al., J. Acoust. Soc. Am. 77, 6 (1985)]; alternately, they are obtained here by using a T‐matrix code. However, a physical explanation of the eigenfrequencies can be given in terms of surface waves circumnavigating the spheroid along a geodesic, and a phase matching condition can be written down which takes the form of an integral, due to the variations of the surface wave propagation constant along the path. A model is used in which the propagation constant is approximated by the known one on a sphere, with the same local radius of curvature along the propagation direction. This condition serves either to obtain the complex eigenfrequencies, or to test the accuracy of eigenfrequencies obtained by other methods. [Supported by NSRDC and ONR.]

Surface waves on a radially stratified earth

It is well known that the normal modes of free oscillations of the earth may be interpreted in terms of surface waves. We elaborate on this connection by demonstrating that a normal mode may be viewed as being physically created by the resonant reinforcement of multiply-circumnavigating surface waves. The dispersion curves for the phase and group velocities of these surface waves may accordingly be determined from the eigenfrequency spectrum of the earth's oscillations, which is done here using the set of eigenfrequencies empirically obtained by Gilbert and Dziewonski. These “empirical” dispersion curves are compared with global surface wave data furnished by a standard earth model, as well as with local surface wave measurements, and some possibly significant differences are found.

Effect of finite ground impedance on the propagation of acoustic pulses

The propagation of an acoustic transient in the vicinity of a finite impedance ground plane has been numerically simulated. A waveform characteristic of a small explosive charge was selected for analysis. Pulse waveforms and amplitudes were computed for propagation distances from 3 to 3000 m, for microphone heights from 0 to 30 m, and for flow resistances from 10 to 1000 g cm−3 s−1. Typical values of atmospheric variables were assumed. Nonlinear propagation effects, atmospheric refraction, and turbulence were excluded from the analysis. This study indicates that finite ground impedance can significantly affect acoustic pulses from explosives. The need to consider ground effects when relating the results of small‐scale explosive tests to larger scale explosions is demonstrated. Finite impedance effects are small (<2 dB) for the pulse shape studied if the numerical distance of the fundamental frequency is less than 0.1. The surface wave term as formulated by Donato [J. Acoust. Soc. Am. 60, 34–39 (1976)] pro...

Diffraction of a spherical wave by an absorbing plane: A general theoretical approach

In outdoor sound propagation, the ground absorption is described by various models such as a locally reacting surface or layer of porous material. For each type of absorbing plane, different authors have developed specific methods to calculate an approximation of the sound pressure. In the present paper a general method is proposed. If the absorbing plane is located at z = 0, and a point source at S(0,0,d), an exact representation of the solution shows that the diffracted field can be decomposed into the sum of (a) the radiation of an image source at S′(0,0,−d); (b) the radiation of a surface source located in the z = −d plane; (c) the z = derivative of the radiation of a surface source located in the same plane. From this exact integral representation of the solution, two series expansions can be derived. The first one, convergent for any source and receiver locations, involves the asymptotic series and a correcting series: the first two or three terms provide a sufficiently accurate approximation for distances from a few wavelengths up to infinity. The second is a Taylor-like series with respect to the vertical distance between the image source S′ and the receiver; it points out the well-known surface wave term, but gives good approximations close to the ground surface, only. Several examples are given: locally reacting surface; finite or infinite thickness layer of porous material; thin elastic plate. Numerical results show the efficiency of these approximations for engineering purposes.

The resonances of a finite‐length fluid cylinder and their interpretation in terms of surface waves

We consider a finite‐length fluid cylinder surrounded by either a very tenuous or a very dense exterior fluid. This amounts to respectively considering either Dirichlet or Neumann boundary conditions on the cylinder's surface. The eigenfrequencies of such finite‐length cylinders are interpreted in this paper as the resonances caused by phase matching of circumferential waves that circumnavigate the cylinder along certain helicoidal Fermat paths, and that get reflected back and forth from its top and bottom flat surfaces. We have obtained the dispersion curves of these circumferential (i.e., “creeping”) waves which are seen to correspond to a series of well‐defined pitch angles of their helix, for different values of the cylinder's length‐to‐radius ratio. We generate and display graphs pertaining to various cylinder sizes, boundary conditions, and pitch angle of each of the resulting surface waves. [H. Überall is also at Catholic University, Washington, DC, and was additionally supported by Code 421 of ONR.]

The theory of resonance scattering in acoustics, nondestructive testing, and geophysics

This paper summarizes recent progress concerning modal and surface‐wave resonances in scattering and reflection of acoustic waves from elastic (or viscoelastic) objects, and of elastic waves from cavities or solid inclusions. Experiments and normal‐mode calculations have revealed a large, often confusing variety of resonance phenomena in both acoustic and elastic‐wave scattering. In collaboration with L. Flax, L. R. Dragonette, G. C. Gaunaurd, and others, we have developed a systematic theory based on the Breit‐Wigner formalism of nuclear resonance scattering, in which the observed resonances can be explained physically, and interpreted in terms of the modal eigenvibrations of the elastic targets. or the contents of the cavity, respectively. Modal scattering amplitudes consist of a nonresonant background with superimposed, and interfering, resonance contributions. The latter can be isolated by subtracting the background, both in the “rigid” and the “soft” limits and in the general intermediate case. The same resonances may be viewed differently, with the mode index being considered a complex variable. This permits interpreting the scattering amplitude in terms of surface waves (“creeping waves”) corresponding to the Regge Poles of Nuclear Physics. We unify the two viewpoints, demonstrating that the resonances of the modal target eigenvibrations correspond to “phase‐matching” of the creeping waves, which occurs when the target's circumference measures an even (for cylinders) or odd (for spheres) integer number of half‐wave lengths. [Supported by ONR Code 421.]