Generalized space-time paraxial acoustic ray tracing

Paraxial ray tracing has gained popularity in seismology and underwater acoustics for modelling the propagation of sound when the medium is stationary and time independent. In this article differential geometry is used to derive a generalized paraxial ray-tracing procedure valid for any fluid media described by a local sound speed and velocity depending arbitrarily on position and time. Geodesic deviation is used to model acoustic beam deformation, and the sectional curvature along a ray to determine convergence and divergence zones in space. The resulting paraxial equations presented here are the most general that can be derived for the acoustic field and apply to any environment including those with time dependence and fluid motion. Applied to layered media the geodesic deviation equation is solved exactly. Some illustrative examples are included.     

The contribution of a lateral wave in simulating low-frequency sound fields in an irregular waveguide with a liquid bottom

A further development of a previously proposed approach to calculating the sound field in an arbitrarily irregular ocean is presented. The approach is based on solving the first-order causal mode equations, which are equivalent to the boundary-value problem for acoustic wave equations in terms of the cross-section method. For the mode functions depending on the horizontal coordinate, additional terms are introduced in the cross-section equations to allow for the multilayer structure of the medium. A numerical solution to the causal equations is sought using the fundamental matrix equation. For the modes of the discrete spectrum and two fixed low frequencies, calculations are performed for an irregular two-layer waveguide model with fluid sediments, which is close to the actual conditions of low-frequency sound propagation in the coastal zone of the oceanic shelf. The calculated propagation loss curves are used as an example for comparison with results that can be obtained for the given waveguide model with the use of adiabatic and one-way propagation approximations.     

Simulation of low-frequency sound propagation in an irregular shallow-water waveguide with a fluid bottom

A further development of a previously proposed approach to calculating the sound field in an arbitrarily irregular ocean is presented. The approach is based on solving the first-order causal mode equations, which are equivalent to the boundary-value problem for acoustic wave equations in terms of the cross-section method. For the mode functions depending on the horizontal coordinate, additional terms are introduced in the cross-section equations to allow for the multilayer structure of the medium. A numerical solution to the causal equations is sought using the fundamental matrix equation. For the modes of the discrete spectrum and two fixed low frequencies, calculations are performed for an irregular two-layer waveguide model with fluid sediments, which is close to the actual conditions of low-frequency sound propagation in the coastal zone of the oceanic shelf. The calculated propagation loss curves are used as an example for comparison with results that can be obtained for the given waveguide model with the use of adiabatic and one-way propagation approximations.     

部分空间相干光束在非Kolmogorov湍流大气中的有效曲率半径

激光在湍流大气中的传输有重要的理论研究和实际应用意义.以高斯-谢尔模型(GSM)光束作为部分空间相干光的典型例,基于非Kolmogorov谱和广义惠更斯-菲涅耳原理, 推导出GSM光束在非Kolmogorov湍流中的有效曲率半径的解析表达式. 重点研究了湍流参数(包括广义指数α,内尺度l₀,和外尺度L₀) 和传输距离z分别对GSM光束有效曲率半径的影响.结果表明, 有效曲率半径R_x(z)随α和z增加先减小然后再增大, 随L₀的减小而增大(3.6<α< 4),随l₀的增加而增大.并对结果做了物理解释.     

一种水平变化波导中声传播问题的耦合模态法

针对介质参数及海底边界水平变化波导中的声传播问题,本文基于多模态导纳法提出一种能量守恒且便于数值稳定求解的耦合模态方法.将声压表示为一组正交完备的本地本征函数之和,对声压满足的Helmholtz方程在本地本征函数上作投影,推导出关于声压模态系数的二阶耦合模态方程组.耦合矩阵直观描述水平变化因素对模态耦合的贡献.为避免直接求解二阶耦合模态方程组可能遇到的数值发散问题,将其重构为两个耦合的一阶演化方程组,引入导纳矩阵并使用Magnus数值积分方法获得稳定的声场解.利用该耦合模态方法数值计算水平变化波导中的声场,并与COMSOL参考解比较,结果表明该耦合模态理论能够精确求解水平变化波导中的点源及分布源传播问题.     

三维浅海环境下孤立子内波对低频声能流的传播影响

针对三维浅海环境下孤立子内波对低频声信号传播特性的影响问题,基于Oxyz坐标系下的三维浅海低频声场有限元计算方法,以声能流为研究对象,仿真分析了内波存在对低频声信号传播特性的影响规律。研究结果表明:受内波影响,在xOz平面,声能流垂直分量的传播偏转角度呈现周期性的起伏规律;随着声源深度的增加,内波对声能流偏转角度的影响深度也随之增加。对xOy平面,当声源位于温跃层以上时,随着接收深度的增加,各深度平面上声能流水平分量的偏转角越大;随着声源深度的增加,内波对各深度平面上声能流的影响逐渐减弱。      

Development of an optimised, standard-compliant procedure to calculate sound transmission loss: numerical measurements

Availability of low-frequency characteristics of sound insulating elements is required in order to achieve efficient control of noise sources and reduced level of annoyance in the low-frequency range. Previous work by the author has addressed the problem of designing an enhanced calculation environment for the estimation of sound Transmission Loss (TL). In this work, numerical prediction of TL of sound insulating structures is performed using a procedure, which is in compliance with the ISO recommendations for acoustic measurements. The room-structure-room finite element representation, employed to solve sound propagation and sound-structure interaction problems, as well as the dynamic coupling of and the sound energy propagation through successive air-structure layers are investigated. Several cases of single-layered plain structures of common sound insulating materials such as steel, glass and aluminium with various thickness values are modelled and the calculated TL is compared with published experimental results. It is shown that although the detailed dynamic response of the structures is not accurately predicted due to uncertain parameters, such as the test-specimens dimension and vaguely known boundary conditions, the octave band averaged TL is sufficiently predicted for the majority of the tested materials. Extension of the method to multi-layered structures is attempted and discrepancies at low frequencies are depicted. Finally, the effect of poor mode distribution of the measurement rooms upon the estimated TL is examined in focus. Comparison is performed between TL values calculated with typical and intensely modified transmission rooms. The low-frequency improvement on measurements, when the second ones are used, is demonstrated.     

Proper orthogonal decomposition and cluster weighted modeling for sensitivity analysis of sound propagation in the atmospheric surface layer

Outdoor sound propagation predictions are compromised by uncertainty and error in the atmosphere and terrain representations, and sometimes also by simplified or incorrect physics. A model's predictive power, i.e., its accurate representation of the sound propagation, cannot be assessed without first quantifying the ensemble sound pressure variability and sensitivity to uncertainties in the model's governing parameters. This paper describes fundamental steps toward this goal for a single-frequency point source. The atmospheric surface layer is represented through Monin-Obukhov similarity theory and the acoustic ground properties with a relaxation model. Sound propagation is predicted with the parabolic equation method. Governing parameters are modeled as independent random variables across physically reasonable ranges. Latin hypercube sampling and proper orthogonal decomposition (POD) are employed in conjunction with cluster-weighted models to develop compact representations of the sound pressure random field. Full-field sensitivity of the sound pressure field is computed via the sensitivities of the POD mode coefficients to the system parameters. Ensemble statistics of the full-field sensitivities are computed to illustrate their relative importance at every down range location. The central role of sensitivity analysis in uncertainty quantification of outdoor sound propagation is discussed and pitfalls of sampling-based sensitivity analysis for outdoor sound propagation are described.     

Computer modeling of sound fields in the ocean with fine-structured inhomogeneities

The results of a computer modeling of sound propagation in the ocean with fine-structured inhomogeneities are presented. The modeling was performed using a wave code based on the wide-angle approximation, which allows one to estimate the effects of sound field perturbations. These effects include the insonification of the geometric shadow zones and the abnormal attenuation of low-frequency sound in the course of its propagation in an oceanic waveguide. Calculations clearly demonstrate that the fine-structured inhomogeneities of the sound velocity considerably affect the sound propagation in the ocean.     

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.     

Generalized tensor ABCD law for an elliptical Gaussian beam passing through an astigmatic optical system in turbulent atmosphere

The propagation of an elliptical Gaussian beam (EGB) through an astigmatic ABCD optical system in a turbulent atmosphere is investigated. An analytical formula for the average intensity of an EGB and a generalized tensor ABCD law for the generalized complex curvature tensor are derived. As an application example, we derived an analytical formula for the average intensity of an elliptical flat-topped beam propagating through an astigmatic ABCD optical system in a turbulent atmosphere. As a numerical example, the focusing properties of an EGB focused by a thin lens in a turbulent atmosphere are studied. It is found that the focused beam at the focal plane becomes a circular Gaussian beam when the atmospheric turbulence is strong enough, and the beam width of the circular Gaussian beam is determined by atmospheric turbulence strength, focal length of the thin lens, and wavelength of the initial beam but is independent of the initial beam widths (i.e., initial intensity distribution).     

等价分布源方法新发展

本文以广义Lighthill方程和广义Green函数为基础给出任意截面管道声传播计算模型,同时应用等价分布源方法建立了包含声衬影响的声传播模型,该方法避开了复杂的管道特征值计算,并在此基础上以积分变换发展了等价分布源方法,免去了声源及观察点匹配时产生的奇异性,使该方法大大简化,易于工程实际计算.此外,本文还给出了特殊截面管的算例.     

Effect of the bulk viscosity on the sound propagation in nonequilibrium suspensions of microparticles in gas

The sound propagation in a mixture of gas with uniformly dispersed solid particles, whose temperature is maintained above that of the gas by an external source, is considered. The dispersion properties of this kind of suspensions are studied, and expressions for the second viscosity and the sound velocity in such suspensions are derived. It is shown that, in a nonequilibrium suspension, the second viscosity may be negative. The ranges of the suspension parameters, for which the propagation of low-frequency sound is impossible, are determined.     

Multiple-array passive acoustic source localization in urban environments

In many situations of interest, obstacles to acoustic wave propagation such as terrain or buildings exist that provide unique challenges to localization. These obstacles introduce multiple propagation paths, reflections, and diffraction into the propagation. In this paper, matched field processing is proposed as an effective method of acoustic localization in a two dimensional scattering environment. Numerical techniques can be used to model complex propagation in a space where analytical solutions are not feasible. Realistically, there is always some uncertainty in model parameters that in turn can adversely affect localization ability. In particular, uncertainty in array location, sound speed, and various parameters affecting inter-array coherence only are investigated. A spatially distributed, multiarray network is shown to mitigate the effects of uncertainty. Multiarray inverse filter processing techniques are evaluated through perturbation of uncertain model parameters. These techniques are more accurate and flexible to implement than other matched field processing methods such as time reversal.     

Generating ultra wide low-frequency gap for transverse wave isolation via inertial amplification effects

Low-frequency transverse wave propagation plays a significant role in the out-of-plane vibration control. To efficiently attenuate the propagation of transverse waves at low-frequency range, this letter proposed a new type phononic beam by attaching inertial amplification mechanisms on it. The wave propagation of the beam with enhanced effective inertia is analyzed using the transfer matrix method. It is demonstrated that the low-frequency gap within inertial amplification effects can possess much wider bandwidth than using the local resonance method, thus is more suitable for designing applications to suppress transverse wave propagation.     

Interfering modes and an axial wave in an underwater sound channel

Experiments on long-range propagation of low-frequency sound that were conducted starting from the mid-1980s indicate a complex character of propagation in an underwater sound channel, in which a source and a receiver are located close to the channel axis. A burst of energy propagating along the axis follows early arrivals, which are well described by the formulas of geometrical acoustics, in plots of acoustic intensity as a function of propagation time and hydrophone depth. This energy burst cannot be described using geometrical acoustics because of caustics with caustic beaks located near the channel axis. Very complex interference processes occur near these caustics. As the distance from the source grows, the dimensions of the interference vicinity increase and start to overlap producing a peculiar “axial wave.” For an arbitrary two-dimensional underwater sound channel, the axial wave can be represented as a sum of the first normal modes and a residue. This conclusion is based on the use of two representations for an acoustic field. The first of them includes the sum of ray components and an axial wave. The second representation consists of ray addends, the sum of the first normal modes, and a residue. Numerical results are obtained for a canonical profile of sound velocity at the frequency of 200 Hz for the distances of 1600–1650 km.     

Effects of sediment acoustic characteristics on low-frequency acoustic field distribution in shallow water

Most of the published literatures on low-frequency underwater sound propagation are focused on the sound propagation features in the water column,while studies on sound propagation features in the sediment layer or the semi-infinite basement are rare.In this paper,based on the wave equation,a computational model for sound energy flux in the sediment layer and the basement as well as in the water column is proposed under a cylindrical coordinate system.On this basis,the effects of various sediment acoustic parameters on the sound energy distribution and the corresponding mechanisms are elaborated through numerical examples and acoustic theory.Simulation results reveal that,in a situation where sediment P-wave speed>water sound speed> sediment S-wave speed,the greater the values of density and P-wave speed in sediment,the more likely it is that the sound energy remains in the water column without leaking to the sea floor.Conversely,the influence of the variation of S-wave speed is reversed.Basement influence on the sound propagation in the fluid layer is approximately negligible if the sediment layer is sufficiently thick.     

Three-dimensional coupled-mode model and characteristics of low-frequency sound propagation in ocean waveguide with seamount topography

Large-scale topography, such as a seamount, substantially impacts low-frequency sound propagation in an ocean waveguide, limiting the application of low-frequency acoustic detecting techniques. A three-dimensional (3D) coupled-mode model is developed to calculate the acoustic field in an ocean waveguide with seamount topography and analyze the 3D effect. In this model, a correction is introduced in the bottom boundary, theoretically making the acoustic field satisfy the energy conservation. Furthermore, a large azimuth angle calculation range is obtained by using the operator theory and higher-order Padé approximation. Additionally, the model has advantages related to the coupling mode and parabolic equation theory. The couplings corresponding to the effects of range-dependent environment are fully considered, and the numerical implementation is kept feasible. After verifying the accuracy and reliability of the model, low-frequency sound propagation characteristics in the seamount environment are analyzed. The results indicate lateral variability in bathymetry can lead to out-of-plane effects such as the horizontal refraction phenomenon, while the coupling effect tends to restore the abnormal sound field and produces acoustic field diffraction behind the seamount. This model effectively considers the effects of the horizontal refraction and coupling, which are proportional to the scale of the seamount.     

Second sound in SrTiO3

We study collective phonon excitations in SrTiO3 by low-frequency light scattering. We employ extended thermodynamics for phonon gas to construct a theoretical spectral function that is applicable regardless of local thermal equilibrium. Our analysis reveals the temperature dependence of tauN, the relaxation time for the momentum-conserving phonon collisions (normal processes), in SrTiO3. These results indicate that the previously reported anomalous soundlike spectrum originates from second sound, which is a wavelike propagation of heat.