Acoustic wave propagation in two-phase heterogeneous porous media

The propagation of an acoustic wave through two-phase porous media with spatial variation in porosity is studied. The evolutionary wave equation is derived, and the propagation of an acoustic wave is numerically analyzed in application to marine sediments with various physical parameters.     

Derivation of a wave equation for pulse propagation beyond a slowly varying envelope approximation

An iterative method is used to derive an accurate weve equation that governs ultrashort pulse propagation in a single mode fibre. In the derivation, the slowly varying evelope approximation (SVEA) is not required. Therefore, the wave equation can be used to describe the propagation of an ultrashort pulse of a few optical cycles. It is found that, compared with the wave equation obtained by making an SVEA, an accurate wave equation has the same coefficients of the linear dispersion terms and different coefficients of the high-order time derivatives of the non-linear terms.     

Acoustic wave propagation simulation in a poroelastic medium saturated by two immiscible fluids using a staggered finite-difference with a time partition method

Based on the three-phase theory proposed by Santos, acoustic wave propagation in a poroelastic medium saturated by two immiscible fluids was simulated using a staggered high-order finite-difference algorithm with a time partition method, which is firstly applied to such a three-phase medium. The partition method was used to solve the stiffness problem of the differential equations in the three-phase theory. Considering the effects of capillary pressure, reference pressure and coupling drag of two fluids in pores, three compressional waves and one shear wave predicted by Santos have been correctly simulated. Influences of the parameters, porosity, permeability and gas saturation on the velocities and amplitude of three compressional waves were discussed in detail. Also, a perfectly matched layer (PML) absorbing boundary condition was firstly implemented in the three-phase equations with a staggered-grid high-order finite-difference. Comparisons between the proposed PML method and a commonly used damping method were made to validate the efficiency of the proposed boundary absorption scheme. It was shown that the PML works more efficiently than the damping method in this complex medium. Additionally, the three-phase theory is reduced to the Biot’s theory when there is only one fluid left in the pores, which is shown in Appendix. This reduction makes clear that three-phase equation systems are identical to the typical Biot’s equations if the fluid saturation for either of the two fluids in the pores approaches to zero. Supported by the Key Program of the National Natural Science Foundation of China (Grant No. 10534040) and the National Natural Science Foundation of China (Grant No. 10674148)     

Reverse wave propagation in a randomly-inhomogeneous medium

Conclusion Therefore, it has convincingly been demonstrated in this paper that the so-called RWF mirror that reverses the radiation wave front even when using a finite aperture will assure elimination of field fluctuations during propagation in media with large-scale scatterers. Both reproduction of the mean intensity distribution and suppression of the intensity fluctuations are assured here in two-pass schemes.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 51–63, November, 1985.     

Time domain numerical modeling of wave propagation in 2D heterogeneous porous media

This paper deals with the numerical modeling of wave propagation in porous media described by Biot’s theory. The viscous efforts between the fluid and the elastic skeleton are assumed to be a linear function of the relative velocity, which is valid in the low-frequency range. The coexistence of propagating fast compressional wave and shear wave, and of a diffusive slow compressional wave, makes numerical modeling tricky. To avoid restrictions on the time step, the Biot’s system is splitted into two parts: the propagative part is discretized by a fourth-order ADER scheme, while the diffusive part is solved analytically. Near the material interfaces, a space–time mesh refinement is implemented to capture the small spatial scales related to the slow compressional wave. The jump conditions along the interfaces are discretized by an immersed interface method. Numerical experiments and comparisons with exact solutions confirm the accuracy of the numerical modeling. The efficiency of the approach is illustrated by simulations of multiple scattering.     

Acoustic wave propagation in bent thin-walled wave guides

Theoretical analysis of sound wave propagation in structures indicates considerable amplitude reduction during transmission through a bent joint, while some build-up can be observed in front of the bend. Every type of transmitted wave (longitudinal and flexural in plane frames) is found to combine with other forms of sound propagation as a result of the deflection of the axis of the wave guide. The screening effect of the bend, in solids with arbitrary viscoelastic properties, is evident even under highly simplified assumptions, such as compatibility and equilibrium. By solving several practical problems, the attenuation due to folding of the structure is compared to the damping effect of the material, with the conclusion that the former contribution is the larger of the two. A pair of examples of insulation analysis of structures is worked out, and the results yield the particle velocity—the first step in determining the radiation pattern. The influence of dense columns in walls, of beams in plates, and of coupling effects in bent structures are examined.     

Acoustic wave propagation in high-pressure system

Recently, substantial attention is paid to the development of methods of generation of pulsations in high-pressure systems to produce pulsating high-speed water jets. The reason is that the introduction of pulsations into the water jets enables to increase their cutting efficiency due to the fact that the impact pressure (so-called water-hammer pressure) generated by an impact of slug of water on the target material is considerably higher than the stagnation pressure generated by corresponding continuous jet. Special method of pulsating jet generation was developed and tested extensively under the laboratory conditions at the Institute of Geonics in Ostrava. The method is based on the action of acoustic transducer on the pressure liquid and transmission of generated acoustic waves via pressure system to the nozzle. The purpose of the paper is to present results obtained during the research oriented at the determination of acoustic wave propagation in high-pressure system. The final objective of the research is to solve the problem of transmission of acoustic waves through high-pressure water to generate pulsating jet effectively even at larger distances from the acoustic source. In order to be able to simulate numerically acoustic wave propagation in the system, it is necessary among others to determine dependence of the sound speed and second kinematical viscosity on operating pressure. Method of determination of the second kinematical viscosity and speed of sound in liquid using modal analysis of response of the tube filled with liquid to the impact was developed. The response was measured by pressure sensors placed at both ends of the tube. Results obtained and presented in the paper indicate good agreement between experimental data and values of speed of sound calculated from so-called "UNESCO equation". They also show that the value of the second kinematical viscosity of water depends on the pressure.     

Electromagnetic wave propagation in a medium with defects

The equations of the electromagnetic field in a solid with defects were obtained and an approximate wave solution was found by the Debye–Rytov method.     

Monte Carlo simulation for millimeter wave propagation and scattering in rain medium

As the operating frequencies of communications systems more higher into the millimeter wave range, the effects of multiple scattering in precipitation media become more significant. This paper treats the problems of electromagnetic multiple scattering in rain medium by the Monte Carlo method. The em wave is regarded as a Markov chain of photon collisions in a medium in which it is scattered and absorbed. For the sake of simplicity, the polarization is not taken into account, the above mentioned problems are described by the scale integro-diffierential equation of transfer. When the plane wave through a random medium with particle size distribution, the technique of weighted average is used to characterize the radiation intensity, including average scattering, absorption coefficients and phase function. The Monte Carlo simulation algorithms are done for the rain attenuation and reflectance at millimeter wavelength region. Our computational results are in good agreement with experimental data of rain attenuation.     

Markovian non-Gaussian approximation for light propagation in a random medium

A theory is presented for wave propagation in a random medium that generalizes the Markovian-Gaussian approximation to the case of a non-Gaussian probability distribution of refractivity fluctuations. A Poissonian model of refractivity fluctuations that are statistically independent in non-overlapping intervals in the x-direction is used. This model turns out to be Gaussian under appropriate conditions. General solutions are obtained for the mean field and the mutual coherence function of a plane, partially coherent incident wave. These solutions contain a new functional parameter, a characteristic function of the amplitude of dielectric permittivity fluctuations, that affects the shape of the coherence function as well as its spectrum.     

Acoustic wave propagation in liquid helium II

Elsewhere [1], using the framework of multipolar continuum mechanics, the authors have discussed a possible alternative to the two-fluid theories for liquid helium 11 and showed that, in the case when the fluid is assumed to be incompressible, second sound waves exist in both the stationary and rotating fluid. Here the constitutive theory presented in the paper cited is extended to include the effects of compressibility and viscosity and a study of these effects on the propagation of small-amplitude waves. 1t is found that the qualitative predictions agree with the experimental observations in helium II.     

Rayleigh mechanism of local elevation of energy in propagation of a shock wave in an active medium

A mechanism of action of a shock wave on an active medium, which leads to an additional energy release source, is considered. This source moves together with the shock wave front and depends on the magnitude and direction of the electric field applied to the plasma and on the current density in the plasma. The study is a continuation of an earlier publication devoted to the propagation of weak shock waves. Here, we consider shock waves of an arbitrary intensity with an arbitrary mechanism of formation of an additional energy contribution due to variation of the parameters of the medium as a result of passage of the shock wave. Special cases of this effect are the propagation of a shock wave in a plasma and detonation burning.     

Acoustic wave propagation in a binary mixture of inviscid fluids

Linearized equations governing the thermo-mechanical behaviour of a binary mixture of inviscid fluids are derived. Restrictions which are sufficient for the equations to have a unique solution are imposed on some of the material constants. The propagation of plane harmonic waves of small amplitude in the mixture is examined and the inequalities are shown to ensure a physically reasonable response. As an application of the theory properties of acoustic waves in a binary mixture of ideal gases are evaluated numerically.     

Elastic wave propagation in a randomly stratified solid medium

Abstract

The mean-field method is used to analyse longitudinal and transverse (both SV- and SH-type) wave propagation in an unbounded randomly stratified solid medium. It is assumed that elastic moduli of the medium are constant while a density is a random function of the cartesian coordinate z. For a case of small density fluctuations, expressions are obtained for z-components of effective propagation vectors of P-, SV- and SH-waves for arbitrary relations between wavelengths and a correlation length of the random inhomogeneities. It is shown, that when the correlation length is small in comparison with the wavelengths, the mean-field attenuation coefficients are proportional to the frequency squared. In this case P- and SV-waves convert into each other. When the correlation length is large in comparison with the wavelengths, the mean-field attenuation coefficients are also proportional to the frequency squared, but in this case P- and SV-waves propagate independently.     

Elastic wave propagation in a randomly stratified solid medium

The mean-field method is used to analyse longitudinal and transverse (both SV- and SH-type) wave propagation in an unbounded randomly stratified solid medium. It is assumed that elastic moduli of the medium are constant while a density is a random function of the cartesian coordinate z. For a case of small density fluctuations, expressions are obtained for z-components of effective propagation vectors of P-, SV- and SH-waves for arbitrary relations between wavelengths and a correlation length of the random inhomogeneities. It is shown, that when the correlation length is small in comparison with the wavelengths, the mean-field attenuation coefficients are proportional to the frequency squared. In this case P- and SV-waves convert into each other. When the correlation length is large in comparison with the wavelengths, the mean-field attenuation coefficients are also proportional to the frequency squared, but in this case P- and SV-waves propagate independently.     

Acoustic boundary layer influence on scale model simulation of sound propagation: Theory and numerical examples

Scale model simulation of sound propagation above a solid surface will give a systematic and calculable error in the predicted sound field, because the acoustic boundary layer above the surface has an apparent admittance which is not invariant under scaling. The typical error is approximately 5 dB depending on the geometrical configuration, scale and frequency. The effect of the acoustic boundary layer admittance is negligible for sound propagation above an acoustically soft surface (e.g., grassland). One may moreover note, with reference to scale model simulation of concert hall acoustics, that the absorption coefficient of a solid surface increases with frequency.