非线性对大气介质中阵列聚焦声场分布影响的研究

基于时域有限差分算法将大气中近似到二阶微小项的非线性声波波动方程进行离散化,得到了模拟采用的差分波动方程.在此基础上,数值模拟了初始声压强弱不同的5个点声源组成的线阵列垂直或斜向辐射的连续正弦波在大气中传播时二维声场的分布情况.将线性条件下的模拟结果与非线性条件下的模拟结果进行比较后发现:弱非线性会对声场的分布和阵列聚焦增益产生一定的影响,使声场分布波形比线性条件下的声场分布波形更加靠近阵列,聚焦效果变差;强非线性会使波形发生更严重畸变,这是由于产生了基频以外的其他频率声波引起的;非线性对斜向传播时声场分布的影响与垂直传播时的影响效果基本相同,但由于斜向辐射时的声波几何扩展造成的轴向声压衰减要大于垂直辐射时的轴向声压衰减,因此聚焦增益和强非线性的影响都将小于垂直辐射时的情况.     

含气泡液体中的非线性声传播

考虑到分布在液体中的气泡是声波在含气泡液体中传播时引起非线性的一个很重要的因素,本文研究了声波在含气泡液体中的非线性传播.将气体含量的影响引入到声波在液体中传播的方程中,从而得到声波在气液混合物中传播的数学模型.通过对该模型进行数值模拟发现,气体含量、驱动声场声压幅值及驱动声场作用时间均会影响到气液混合物中的声场分布及声压幅值大小.液体中的气泡会"阻滞"液体中声场的传播并将能量"聚集"在声源附近.对于连续大功率的驱动声场来说,液体中的气泡会"阻滞"气液混合物中声场及其能量的传播.     

Sound propagation and scattering in media with random inhomogeneities of sound speed, density and medium velocity

This review presents both classical and new results of the theory of sound propagation in media with random inhomogeneities of sound speed, density and medium velocity (mainly in the atmosphere and ocean). An equation for a sound wave in a moving inhomogeneous medium is presented, which has a wider range of applicability than those used before. Starting from this equation, the statistical characteristics of the sound field in a moving random medium are calculated using Born-approximation, ray, Rytov and parabolic-equation methods, and the theory of multiple scattering. The results obtained show, in particular, that certain equations previously widely used in the theory of sound propagation in moving random media must now be revised. The theory presented can be used not only to calculate the statistical characteristics of sound waves in the turbulent atmosphere or ocean but also to solve inverse problems and develop new remote-sensing methods. A number of practical problems of sound propagation in moving random media are listed and the further development of this field of acoustics is considered.     

Distortion of waves with profile discontinuities in the medium with a periodic transverse inhomogeneity distribution

For the purpose of describing the joint influence of nonlinear effects and refractive inhomogeneities on the evolution of intense acoustic waves, a model of the medium the local velocity of sound of which is periodic in the transverse direction and decreases in the propagation direction, which generalizes the known models of the layered medium and of the infinitesimally thin phase screen, is proposed. An exact solution is found for the wave with arbitrary initial conditions: time profile and transverse profile. The spatial wave structure in the inhomogeneous medium is calculated; it is shown that narrow high-amplitude regions are formed and the rate of nonlinear effect accumulation changes. It is shown that the amplitude of the wave at long distances from the source may differ little from its initial value due to compensation for the effects of nonlinear attenuation and of focusing by inhomogeneities. Possibilities of amplification of intense waves depending on the proportion between parameters of the wave and those of the inhomogeneous medium are studied.     

Sound propagation and scattering in media with random inhomogeneities of sound speed,density and medium velocity

Abstract

This review presents both classical and new results of the theory of sound propagation in media with random inhomogeneities of sound speed, density and medium velocity (mainly in the atmosphere and ocean). An equation for a sound wave in a moving inhomogeneous medium is presented, which has a wider range of applicability than those used before. Starting from this equation, the statistical characteristics of the sound field in a moving random medium are calculated using Born-approximation, ray, Rytov and parabolic-equation methods, and the theory of multiple scattering. The results obtained show, in particular, that certain equations previously widely used in the theory of sound propagation in moving random media must now be revised. The theory presented can be used not only to calculate the statistical characteristics of sound waves in the turbulent atmosphere or ocean but also to solve inverse problems and develop new remote-sensing methods. A number of practical problems of sound propagation in moving random media are listed and the further development of this field of acoustics is considered.     

Statistical properties of nonlinear diffracting <Emphasis Type="Italic">N</Emphasis>-wave behind a random phase screen

Propagation of high amplitude N-wave behind a random phase screen is modeled based on the Khokhlov-Zabolotskaya-Kuznetsov equation. One-dimensional random phase screens with Gaussian power spectrum density are considered. The effects of nonlinear propagation, random focusing, and diffraction on the statistical properties of the acoustic field behind the screen, including propagation through caustics and beyond caustics, are analyzed. Statistical distributions and mean values of the acoustic field parameters obtained within the developed diffraction model and using nonlinear geometrical acoustics approach are compared.     

On the appearance of caustics for plane sound-wave propagation in moving random media

In this paper we derive expressions for the probability densities of the appearance of the first caustic for a plane sound wave propagating in moving random media. Our approach generalizes the previous work by White et al. and Klyatskin in the case of motionless media. It allows us to calculate analytically the probability density functions for two- and three-dimensional media and to express these functions in terms of the diffusion coefficient. Explicit equations are given for Gaussian and von Karman spectra of velocity fluctuations. If the random scalar or vectorial fluctuations of the medium have the same contribution to the refractive-index fluctuations, we demonstrate that in a moving medium caustics appear at shorter distances than in a non-moving one. The two-dimensional version of the theory is tested by numerical simulations in the case of velocity fluctuations with Gaussian spectra. Numerical results are in very good agreement with the theoretical predictions.     

Modeling the propagation of nonlinear three-dimensional acoustic beams in inhomogeneous media

A three-dimensional model of the forward propagation of nonlinear sound beams in inhomogeneous media, a generalized Khokhlov-Zabolotskaya-Kuznetsov equation, is described. The Texas time-domain code (which accounts for paraxial diffraction, nonlinearity, thermoviscous absorption, and absorption and dispersion associated with multiple relaxation processes) was extended to solve for the propagation of nonlinear beams for the case where all medium properties vary in space. The code was validated with measurements of the nonlinear acoustic field generated by a phased array transducer operating at 2.5 MHz in water. A nonuniform layer of gel was employed to create an inhomogeneous medium. There was good agreement between the code and measurements in capturing the shift in the pressure distribution of both the fundamental and second harmonic due to the gel layer. The results indicate that the numerical tool described here is appropriate for propagation of nonlinear sound beams through weakly inhomogeneous media.     

Nonlinear and diffraction effects in propagation of N-waves in randomly inhomogeneous moving media

Finite amplitude acoustic wave propagation through atmospheric turbulence is modeled using a Khokhlov-Zabolotskaya-Kuznetsov (KZK)-type equation. The equation accounts for the combined effects of nonlinearity, diffraction, absorption, and vectorial inhomogeneities of the medium. A numerical algorithm is developed which uses a shock capturing scheme to reduce the number of temporal grid points. The inhomogeneous medium is modeled using random Fourier modes technique. Propagation of N-waves through the medium produces regions of focusing and defocusing that is consistent with geometrical ray theory. However, differences up to ten wavelengths are observed in the locations of fist foci. Nonlinear effects are shown to enhance local focusing, increase the maximum peak pressure (up to 60%), and decrease the shock rise time (about 30 times). Although the peak pressure increases and the rise time decreases in focal regions, statistical analysis across the entire wavefront at a distance 120 wavelengths from the source indicates that turbulence: decreases the mean time-of-flight by 15% of a pulse duration, decreases the mean peak pressure by 6%, and increases the mean rise time by almost 100%. The peak pressure and the arrival time are primarily governed by large scale inhomogeneities, while the rise time is also sensitive to small scales.     

DISCRETE HUYGENS' MODELLING APPROACH TO WAVE PROPAGATIONS IN A HOMOGENEOUS ELASTIC FIELD

The application of the discrete Huygens' modelling has been discussed for acoustic wave propagation problems, in which the scalar wave field problems have been focused. The present paper extends the application of the modelling to the elastic wave propagation in a homogeneous elastic medium in which two types of waves, the longitudinal wave and the shear wave, are independent except at the boundary. Each wave can be treated like a scalar wave until the two waves reach the boundary where they couple so as to satisfy the displacement or stress boundary condition. We propose the approach confining ourselves to the two-dimensional field. Some examples are demonstrated, whose solutions are compared with the vectorial wave modelling and finite difference modelling solutions whenever they are available.     

On the velocity of propagation of a signal in nonlinear optical media

The maximum velocity of propagation of a signal, which is defined as the velocity of propagation of the wave front, is considered for electromagnetic waves in nonlinear media. It is shown that the magnitude of velocity is determined to a considerable extent on the form of the constitutive equation defining the relation between the polarization of the medium with the radiation field strength. In the noninertial nonlinearity model, this velocity may be smaller (in media with self-focusing nonlinearity) or larger (defocusing nonlinearity) than the velocity of light in vacuum. For real nonlinear media, for which the inertia of their response is taken into account, the wave front velocity coincides with the velocity of light in vacuum.     

Propagation of acoustic wave in viscoelastic medium permeated with air bubbles

Based on the modification of the radial pulsation equation of an individual bubble, an effective medium method (EMM) is presented for studying propagation of linear and nonlinear longitudinal acoustic waves in viscoelastic medium permeated with air bubbles. A classical theory developed previously by Gaunaurd (Gaunaurd GC and \"{U}berall H, {\em J. Acoust. Soc. Am}., 1978; 63: 1699--1711) is employed to verify the EMM under linear approximation by comparing the dynamic (i.e. frequency-dependent) effective parameters, and an excellent agreement is obtained. The propagation of longitudinal waves is hereby studied in detail. The results illustrate that the nonlinear pulsation of bubbles serves as the source of second harmonic wave and the sound energy has the tendency to be transferred to second harmonic wave. Therefore the sound attenuation and acoustic nonlinearity of the viscoelastic matrix are remarkably enhanced due to the system's resonance induced by the existence of bubbles.     

Experimental investigation of the travel-time variance of an acoustic wave propagating through the grid-generated turbulence

An experimental technique for the investigation of the behaviour of acoustic wave propagation through a turbulent medium is discussed. The present study utilizes the ultrasonic travel-time technique to diagnose a grid-generated turbulence. Travel-time variance is studied versus mean flow velocity, travel distance and outer turbulence scale. The effect of thermal fluctuations, which result in fluctuations of sound speed, is studied using a heated-grid experiment. Experimental data obtained using ultrasonic technique confirm numerical and theoretical predictions of nonlinear increase of the travel-time variance with propagation distance, which could be connected to the occurrence of caustics. The effect of turbulent intensity on the travel-time variance and appearance of caustics is studied. It is demonstrated experimentally that the higher turbulence intensity leads to the shorter distance, at which the first caustic occurs. The probability density for caustics appearance is analysed against the measured wave amplitude fluctuations. The analysis reveals that the region of high-amplitude fluctuations corresponds to the region where the probability of formation of random caustics differs from zero. Experimental results are in very good agreement with theoretical and numerical predictions.     

Nonlinear shear wave interaction in soft solids

This paper describes nonlinear shear wave experiments conducted in soft solids with transient elastography technique. The nonlinear solutions that theoretically account for plane and nonplane shear wave propagation are compared with experimental results. It is observed that the cubic nonlinearity implied in high amplitude transverse waves at f(0)=100 Hz results in the generation of odd harmonics 3f(0), 5f(0). In the case of the nonlinear interaction between two transverse waves at frequencies f(1) and f(2), the resulting harmonics are f(i)+/-2f(j)(i,j=1,2). Experimental data are compared to numerical solutions of the modified Burgers equation, allowing an estimation of the nonlinear parameter relative to shear waves. The definition of this combination of elastic moduli (up to fourth order) can be obtained using an energy development adapted to soft solid. In the more complex situation of nonplane shear waves, the quadratic nonlinearity gives rise to more usual harmonics, at sum and difference frequencies, f(i)+/-f(j). All components of the field have to be taken into account.     

Mean field of a low-frequency sound wave propagating in a fluctuating ocean

Statistical characteristics of low-frequency sound waves propagating over long distances in a fluctuating ocean are important for many practical problems. In this paper, using the theory of multiple scattering, the mean field of a low-frequency sound wave was analytically calculated. In these calculations, the ratio of the sound wavelength and the scale of random inhomogeneities can be arbitrary. Furthermore, the correlation function of inhomogeneities is expressed in terms of a modal spectrum (e.g., internal waves modes). The obtained mean sound field is expressed as a sum of normal modes that attenuate exponentially. It is shown that the extinction coefficients of the modes are linearly related to the spectrum of random inhomogeneities in the ocean. Measurements of the extinction coefficients can therefore be used for retrieving this spectrum. The mean sound field is calculated for both 3D and 2D geometries of sound propagation. The results obtained can be used to study the range of applicability of the 2D propagation model.     

Statistics of caustics in an underwater sound channel

The numerical-analytical phase screen method is used to analyze the statistics of the density of caustics in an underwater sound channel with large-scale random inhomogeneities. Different cases of wave propagation direction with respect to the channel axis are considered, and the influence of the inhomogeneity correlation radius is investigated.     

Nonlinear propagation and control of acoustic waves in phononic superlattices

The propagation of intense acoustic waves in a one-dimensional phononic crystal is studied. The medium consists in a structured fluid, formed by a periodic array of fluid layers with alternating linear acoustic properties and quadratic nonlinearity coefficient. The spacing between layers is of the order of the wavelength, therefore Bragg effects such as band gaps appear. We show that the interplay between strong dispersion and nonlinearity leads to new scenarios of wave propagation. The classical waveform distortion process typical of intense acoustic waves in homogeneous media can be strongly altered when nonlinearly generated harmonics lie inside or close to band gaps. This allows the possibility of engineer a medium in order to get a particular waveform. Examples of this include the design of media with effective (e.g., cubic) nonlinearities, or extremely linear media (where distortion can be canceled). The presented ideas open a way towards the control of acoustic wave propagation in nonlinear regime.     

Effect of shallow water internal waves on ocean acoustic striation patterns

Contour plots of underwater acoustic intensity, mapped in range and frequency, often exhibit striations. It has been claimed that a scalar parameter 'beta', defined in terms of the slope of the striations, is invariant to the details of the acoustic waveguide. In shallow water, the canonical value is β=1. In the present paper, the waveguide invariant is modelled as a distribution rather than a scalar. The effects of shallow water internal waves on the distribution are studied by numerical simulation. Realizations of time-evolving shallow water internal wave fields are synthesized and acoustic propagation simulated using the parabolic equation method. The waveguide invariant distribution is tracked as the internal wave field evolves in time. Both random background internal waves and more event-like solitary internal waves are considered.     

The nonlinear propagation of acoustic waves in a viscoelastic medium containing cylindrical micropores

Based on an equivalent medium approach, this paper presents a model describing the nonlinear propagation of acoustic waves in a viscoelastic medium containing cylindrical micropores. The influences of pores' nonlinear oscillations on sound attenuation, sound dispersion and an equivalent acoustic nonlinearity parameter are discussed. The calculated results show that the attenuation increases with an increasing volume fraction of micropores. The peak of sound velocity and attenuation occurs at the resonant frequency of the micropores while the peak of the equivalent acoustic nonlinearity parameter occurs at the half of the resonant frequency of the micropores. Furthermore, multiple scattering has been taken into account, which leads to a modification to the effective wave number in the equivalent medium approach. We find that these linear and nonlinear acoustic parameters need to be corrected when the volume fraction of micropores is larger than 0.1%.