Wave Propagation in a Medium with Random, Spheroidal Inhomogeneities

An acoustic wave propagating under water experiences fluctuations in phase and amplitude attributable, in the main, to scattering from inhomogeneities arising from variations in the temperature field. Since “patches of thermal inhomogeneity” in the sea are generally regarded as lenticular in shape, it is the purpose of this paper to extend, for both plane and spherical sound waves, contemporary wavefluctuation theory to include the circumstance of spheroidal inhomogeneities. Mean-square amplitude and phase fluctuations are considered for acoustic waves propagating in a statistically uniform medium in which random deviations of the refractive index are small. Large-scale inhomogeneities of arbitrary spheroidal shape are treated, and the influence of transmitter-to-receiver range, acoustic wavelength, and “patch” dimensions on variations in waveamplitude and phase is derived for this general case. Particular attention is given the high-frequency ray limit (Bergmann region) and the low-frequency (Fraunhofer diffraction) region. The significant effects on wavefluctuations of nonspherical inhomogeneities are compared for plane and spherical acoustic waves. [This work was supported by the LMSC Independent Research Program.]

A theoretical study is presented of the mutual correlation between amplitude and phase fluctuations when an acoustic (or electromagnetic) wave propagates in a random medium whose correlation function for refractive index is spheroidal-Gaussian. Amplitude-phase correlations are considered for both plane and spherical waves transmitted through a statistically isotropic medium in which the deviations of refractive index about a mean are small. Large-scale inhomogeneities of arbitrary spheroidal shape are treated, and transmitter-to-receiver ranges are taken as large in comparison with the refractive-index correlation length in the transmitter-receiver plane. Comparison is made between the cases of spherical and nonspherical inhomogeneities, for both plane and spherical acoustic waves. The low- and high-frequency extremes of the theory are given special note.

The Perseverance rover is carrying out an original acoustic experiment on Mars: the SuperCam microphone records the spherical acoustic waves generated by laser sparks at distances from 2 m to more than 8 m. These N-shaped acoustic waves scatter from the multiple local heterogeneities of the turbulent atmosphere. Therefore, large and random fluctuations of sound travel time and intensity develop as the waves cross the medium. The variances of the travel times and the scintillation index (normalized variance of the sound intensity) are studied within the mathematical formalism of the propagation of spherical acoustic waves through thermal turbulence to infer statistical properties of the Mars atmospheric temperature fluctuation field. The comparison with the theory is made by simplifying assumptions that do not include wind fluctuations and diffraction effects. Two Earth years (about one Martian year) of observations acquired during the maximum convective period (10:00-14:00 Mars local time) show a good agreement between the dataset and the formalism: the travel time variance diverges from the linear Chernov solution exactly where the density of occurrence of the first caustic reaches its maximum. Moreover, on average, waves travel faster than the mean speed of sound due to a fast path effect, which is also observed on Earth. To account for the distribution of turbulent eddies, several power spectra are tested and the best match to observation is obtained with a generalized von Karman spectrum with a shallower slope than the Kolmogorov cascade, ϕ(k)∝(1+k2L2)-4/3. It is associated with an outer scale of turbulence, L, of 11 cm at 2 m above the surface and a standard deviation of 6 K over 9 s for the temperature. These near-surface atmospheric properties are consistent with a weak to moderate wave scattering regime around noon with little saturation. Overall, this study presents an innovative and promising methodology to probe the near-surface atmospheric turbulence on Mars.

Oil pipeline leakage will not only cause economic losses, but also pollute the environment, so the leakage detection of pipelines is very important. The acoustic wave method is widely used in pipeline leak detection, and the leak acoustic signal collected by the acoustic wave sensor often contains a lot of noise, which makes it impossible to accurately determine the inflection point of the signal curve and reduces the accuracy of pipeline leak detection. This paper proposes a denoising algorithm based on mutual information optimization complete ensemble empirical mode decomposition with adaptive noise combined with cross-spectral analysis. Compared with other methods, this method can accurately select the effective intrinsic modal function for signal reconstruction, the denoising effect is more obvious, and the original information is preserved to a greater extent. Acoustic waves are attenuated during the propagation process, and will be affected by factors such as pipe connection ports and elbows, making it impossible to accurately determine the amplitude of acoustic waves around the pipeline. According to the propagation characteristics of acoustic waves and various factors that affect the propagation of acoustic waves, this paper establishes a model for calculating the amplitude of acoustic waves, which can accurately determine the amplitude of acoustic waves everywhere in the pipeline. Finally, according to the model, the relationship between pipeline characteristics and detectable leakage rate is analysed. Field experiments show that the proposed model is accurate and the denoising algorithm is efficient. The minimum detectable leakage rate of the oil pipeline can reach 0.43% when the acoustic wave method is used for leak detection.

The propagation of acoustic plane and line-polarized waves in an isotropic solid containing random cavities is studied theoretically and experimentally. The effect of the cavities on the energy density and macroscopic propagation parameters of the acoustic waves is considered and the relationships between the cavities volume concentration, their average dynamic shape factor and the dynamic overall stiffness moduli of the solid are derived in the long wave approximation.

In an array of microbarographs propagation characteristics of pressure fluctuations have been studied qualitatively. For one station the pressure data was digitized. It was found that acoustic and gravity waves can easily be distinguished on the recordings. The diurnal variation of the amplitude of acoustic waves was found to be mainly due to windinduced turbulence. There are highly significant correlations between the amplitude of both acoustic and gravity waves and classical meteorological parameters which can be summarized as follows: “the better the weather, the smaller the amplitude.” Under Foehn conditions the amplitude of gravity waves is increased while acoustic waves are highly damped.

Short pulsed laser induced single acoustic wave generation, propagation, interaction with rigid structures, and focusing in water are experimentally and numerically studied. A large area short duration single plane acoustic wave was generated by the thermoelastic interaction of a homogenized nanosecond pulsed laser beam with a liquid-solid interface and propagated at the speed of sound in water. Laser flash schlieren photography was used to visualize the transient interaction of the plane acoustic wave with various submerged rigid structures [(a) a single block, (b) double blocks, (c) 33° tilted single block, and (d) concave cylindrical acoustic lens configurations]. Excellent agreement between the experimental results and numerical simulation is observed. Our simulation results demonstrate that the laser induced planar acoustic wave can be focused down to several tens of micron size and several bars in pressure.

The present article is a theoretical study of the combined propagation of acoustic and internal waves of finite amplitude in a (horizontally, say) stratified fluid. The linear theory of small amplitude waves predicts that the two waves (i.e., the fluctuations in acoustic pressure and in vertical particle velocity or displacement) are in general coupled. The waves are decoupled whenever the typical wavenumbers are large compared with the inverse of the scale height for the stratification. Furthermore, a horizontally propagating acoustic wave with zero vertical particle displacement (or velocity), when this is possible, is always decoupled from the internal waves, according to linear theory. In a weakly nonlinear theory, however, the waves may be coupled. A time independent radiation pressure is formed within a standing, horizontally directed acoustic wave, which produces a stationary vertical displacement of the particles. Experimental evidence of this effect has been reported elsewhere [1].

We study the high-frequency propagation of acoustic plane and spherical waves in random media. With the geometrical optics and the perturbation approach, we obtain the travel-time mean and travel-time variance at the second order. The main hypotheses are the Gaussian distribution of the acoustic speed perturbation and a factorized form for its correlation function. The second-order travel-time variance explains the nonlinear behaviour at large propagation distance observed with numerical experiments based on ray tracing. Usually, homogeneity and isotropy of the refractive index are considered. Using the geometrical anisotropy hypothesis we extend the theory to a general class of statistically anisotropic random media.

The objective of this investigation is to characterize a quasi-standing-wave pattern having a wavelength two orders of magnitude smaller than the corresponding acoustic wavelength, and relate it to the presence of: a) a downstream travelling wave due to vortical structures generated in a free shear layer, and b) downstream and upstream propagating acoustic waves. In this experiment, the vortical structures were generated by flow past an axisymmetric cavity and their influence extended downstream through the exhaust pipe. The amplitudes of the acoustic waves were associated with Helmholtz resonance of the upstream settling chamber. A linear theory models well the measured amplitude and phase distributions of the fluctuating velocity in the core flow. As system resonance is approached, the ratio of vortex wave amplitude to acoustic wave amplitude decreases. The consequence is an increase in the magnitude and gradient of the phase change across the node, or amplitude minimum, of the resultant standing-wave pattern. In addition, the peak-to-peak amplitude of the quasi-standing-wave increases. A variety of internal (and external) flow systems, including unsteady phenomena in wind tunnels, may be subject to this flow mechanism when the frequency of coherent vortex formation in the test section lies near the Helmholtz resonance frequency of the upstream settling (or plenum) chamber.

Hydrodynamic shock wave propagation after electrical breakdown

Techniques of scanning acoustic microscopy generally rely on local variations of such solid state parameters influencing generation or propagation of acoustic waves. Depending on the manner of impressing acoustic waves into the sample various methods are distinguished. In conventional scanning acoustic microscopy ultrasound is generated by a lens-transducer arrangement outside the sample and focussed onto or below its surface. Changes in the propagation of this ultrasound wave, like absorption and reflexion or temporal propagation delays, enable analysis of the mechanical or elastic response. At very high frequencies and with additional time-resolving detection techniques applications of this technique to surface analysis become possible. Other scanning acoustic microscopes imply the generation of sound or ultrasound directly within the sample itself due to the impact of temporarily modulated particle or photon beams. These are presently laser, electron, or ion beams. With these methods the acoustic signal as detected by a transducer attached to the sample is on principle affected by propagation properties, too, but it is dominated by local changes of the generation process for the acoustic wave, mainly because the frequency ranges used presently are associated with very long acoustic wavelengths. Depending on the physical nature of the primary probe used many sound generation mechanisms are given resulting in a large amount of different applications. By adjusting the probe parameters in a suitable manner the sound generation process can be confined to the direct vicinity of the specimen surface, which makes this technique feasible for surface characterization. The principles of the various techniques are described, and their usability for surface analysis is discussed.

An exact analytic solution of the problem of diffraction of a plane acoustic wave on a cone of arbitrary aperture angle was obtained and studied in [1]. For the case of spherical wave diffraction on a cone a formula is known [2] which relates the solutions of the spherical and plane wave diffraction problems. This study will employ the results of [1, 2] to derive and investigate an exact analytical solution of the problem of diffraction of a spherical acoustic wave on a cone of arbitrary aperture angle. Results of numerical calculations will be presented and compared with analogous results for a plane wave.

The accuracy of the first- and second-order rational parabolic approximations of the ‘‘vertical’’ slowness and the nature of the artifacts associated with them in the space-time solutions to the acoustic wave equations in a fluid medium are investigated. In particular, the reflection of an impulsive, point-source generated, spherical wave against the boundary with a medium with a higher wave speed is analyzed. From the space-time Green’s functions in the relevant two-media configuration, evaluated with the aid of the modified Cagniard method, it is found that, instead of generating the real, physical head wave, the approximations generate artificial head-wavelike arrivals. The analysis makes explicit in which regions of space and in which time interval the artifacts show up and of what nature they are. Numerical results are presented.

Nonlinear characteristic boundary conditions based on nonlinear multidimensional characteristics are proposed for 2‐ and 3‐D compressible Navier–Stokes equations with/without scalar transport equations. This approach is consistent with the flow physics and transport properties. Based on the theory of characteristics, which is a rigorous mathematical technique, multidimensional flows can be decomposed into acoustic, entropy, and vorticity waves. Nonreflecting boundary conditions are derived by setting corresponding characteristic variables of incoming waves to zero and by partially damping the source terms of the incoming acoustic waves. In order to obtain the resulting optimal damping coefficient, analysis is performed for problems of pure acoustic plane wave propagation and arbitrary flows. The proposed boundary conditions are tested on two benchmark problems: cylindrical acoustic wave propagation and the wake flow behind a cylinder with strong periodic vortex convected out of the computational domain. This new approach substantially minimizes the spurious wave reflections of pressure, density, temperature, and velocity as well as vorticity from the artificial boundaries, where strong multidimensional flow effects exist. The numerical simulations yield accurate results, confirm the optimal damping coefficient obtained from analysis, and verify that the method substantially improves the 1‐D characteristics‐based nonreflecting boundary conditions for complex multidimensional flows. Copyright © 2009 John Wiley & Sons, Ltd.