Exact solution of three-dimensional acoustic field in a wedge with perfectly reflecting boundaries

An exact approach is presented to compute the three-dimensional(3D) acoustic field in a homogeneous wedge-shaped ocean with perfectly reflecting boundaries. This approach applies the Fourier synthesis technique, which reduces a 3D point-source ideal wedge problem into a sequence of two-dimensional(2D) line-source ideal wedge problems, whose analytical solution is well established. A comparison of numerical efficiency is provided between this solution and the solution proposed by Buckingham,which is obtained by a sequence of integral transforms. The details of numerical implementation of these two solutions are also given. To validate the present approach and at the same time compare numerical efficiency between this approach and Buckingham's analytical solution, two numerical examples are considered. One is the Acoustical Society of America(ASA) benchmark wedge problem and the other is a wide-angle wedge problem. Numerical results indicate that the present approach is efficient and capable of providing accurate 3D acoustic field results for arbitrary receiver locations, and hence can serve as a benchmark model for sound propagation in a homogeneous wedge-shaped ocean.     

A three-dimensional coupled-mode model for the acoustic field in a two-dimensional waveguide with perfectly reflecting boundaries

This paper presents a three-dimensional(3D) coupled-mode model using the direct-global-matrix technique as well as Fourier synthesis. This model is a full wave, two-way three-dimensional model, and is therefore capable of providing accurate acoustic field solutions. Because the problem of sound propagation excited by a point source in an ideal wedge with perfectly reflecting boundaries is one of a few three-dimensional problems with analytical solutions, the ideal wedge problem is chosen in this work to validate the presented three-dimensional model. Numerical results show that the field results by analytical solutions and those by the presented model are in excellent agreement, indicating that the presented model can serve as a benchmark model for three-dimensional sound propagation problems involving a planar two-dimensional geometry as well as a point source.     

水平变化双层波导声传播问题的耦合简正波解

为了验证现有模型的精度,导出了全反射下边界双层波导中简正波耦合矩阵的解析表达式,并将其应用到全局矩阵耦合简正波模型(Direct Global Matrix Coupled-Mode)中,使得该模型可以提供水平变化双层波导问题的标准解。文中首先利用COUPLE的简正波及耦合矩阵数值解验证了该简正波及耦合矩阵解析表达式的正确性;其次,采用改进的DGMCM模型求解了双层波导海山声传播损失,结果表明,改进后的DGMCM模型可以非常精确地求解水平变化双层波导问题,可作为求解此类问题的标准模型使用。     

Selection of modes in a shallow sea by using a vertical antenna array

The experimental data on selecting the modes in a shallow sea (the Barents Sea) on 17-and 8-km-long paths are presented. The data are obtained with the use of a 93-m-long vertical receiving array of 32 hydrophones and a point sound source transmitting a pulsed signal with linear frequency modulation in a frequency band of 100–300 Hz. The experimental selection of modes is based on the structure of normal waves in a waveguide with a perfectly reflecting impedance bottom. The bottom impedance for different modes is determined from the experiment. A pressure-release bottom and a bottom with an impedance that is intermediate between the pressure-release and rigid cases correspond to the first mode and the higher modes, respectively. The amplitudes of the modes and their directivity are determined. On the basis of the mode dispersion data and the comparison of the mode contents observed at distances of 8 and 17 km, it is concluded that higher modes are generated at the distances from 8 to 17 km.     

On the Method of Source Images for the Wedge Problem Solution in Ocean Acoustics: Some Corrections and Appendices

In this study the method of source images for the problem of sound propagation in a penetrable wedge [G. Deane and M. Buckingham, J. Acoust. Soc. Am. 93 (1993) 1319–1328] is revisited. This solution is very important three-dimensional (3D) benchmark in computational underwater acoustics, since a wedge bounded from above by the sea surface and overlying a sloping penetrable bottom is the simplest model of a shallow-sea waveguide near the coastline. The corrected formulae for the positions of the source images and bottom images are presented together with the explanation of their derivation. The problem of branch choice in the reflection coefficient is thoroughly discussed, and the corresponding explicit formulae are given. In addition, numerical validation of the proposed branch choice schemes and the resulting wedge problem solutions are presented. Finally, source images solution is computed for a series of examples with different ratios of shear and bulk moduli in the bottom. The interplay between the acoustic-elastic waves coupling and the horizontal refraction in the wedge is demonstrated.     

一种水平变化可穿透波导中声传播问题的耦合简正波方法

通过利用标准简正波程序KRAKEN计算本地简正波解及耦合矩阵, 进一步发展了求解水平变化波导中声场的全局矩阵耦合简正波方法(Luo et al., "A numerically stable coupled-mode formulation for acoustic propagation in range-dependent waveguides," Sci. China-Phys. Mech. Astron. 55, 572 (2012)), 使得该方法可以处理具有可穿透海底及随深度变化声速剖面等实际问题, 并提供声场的完全双向解. 本文还给出了双层波导中耦合矩阵的解析表达式, 并利用其验证了本方法中耦合矩阵数值算法的精度. 最后, 利用改善后的全局矩阵耦合简正波模型(DGMCM)计算了美国声学学会(ASA)提出的可穿透楔形波导标准问题, 将所得数值解与参考解比较, 结果表明DGMCM方法可以精确处理水平变化波导中声传播实际问题. 关键词： 耦合简正波理论 全局矩阵方法 可穿透楔形波导     

A theoretical and numerical resolution of an acoustic multiple scattering problem in three-dimensional case

This paper develops an analytical solution for sound, electromagnetic or any other wave propagation described by the Helmholtz equation in three-dimensional case. First, a theoretical investigation based on multipole expansion method and spherical wave functions was established, through which we show that the resolution of the problem is reduced to solving an infinite, complex and large linear system. Second, we explain how to suitably truncate the last infinite dimensional system to get an accurate stable and fast numerical solution of the problem. Then, we evaluate numerically the theoretical solution of scattering problem by multiple ideal rigid spheres. Finally, we made a numerical study to present the “Head related transfer function” with respect to different physical and geometrical parameters of the problem.     

浅海波导中目标散射的简正波-Kirchhoff近似混合方法

提出了计算浅海波导中复杂目标散射的数值方法:简正波-Kirchhoff近似混合方法。通过把目标散射的Kirchhoff近似方法和简正波声传播模型相结合,可对大尺寸复杂目标在浅海波导中的散射声场进行计算。以浅海波导中刚性球体散射的解析解为标准解验证了本方法,说明简正波-Kirchhoff近似混合方法是有一定计算精度的工程预报方法。数值计算Pekeris浅海波导中球体目标散射声场在深度-频率平面和距离-频率平面上的二维干涉结构及其与自由空间中的差异。进而通过FFT获得目标时域回波随深度的分布图,分析浅海波导中目标姿态、声速剖面对Benchmark潜艇目标散射的影响。      

Propagation in an elastic wedge using the virtual source technique

The virtual source technique, which is based on the boundary integral method, provides the means to impose boundary conditions on arbitrarily shaped boundaries by replacing them by a collection of sources whose amplitudes are determined from the boundary conditions. In this paper the virtual source technique is used to model propagation of waves in a range-dependent ocean overlying an elastic bottom with arbitrarily shaped ocean-bottom interface. The method is applied to propagation in an elastic Pekeris waveguide, an acoustic wedge, and an elastic wedge. In the case of propagation in an elastic Pekeris waveguide, the results agree very well with those obtained from the wavenumber integral technique, as they do with the solution of the parabolic equation (PE) technique in the case of propagation in an acoustic wedge. The results for propagation in an elastic wedge qualitatively agree with those obtained from an elastic PE solution.     

Noise reduction in tunnels by hard rough surfaces

This paper examines the feasibility of using two-dimensional hard rough surfaces to reduce noise levels in traffic tunnels with perfectly reflecting boundaries. First, the Twersky boss model is used to estimate the acoustic impedance of a hard rough surface. Second, an image source model is then used to compute the propagation of sound in a long rectangular enclosure with finite impedance. The total sound fields are calculated by summing the contributions from all image sources coherently. Two model tunnels are built to validate the proposed model experimentally. Finally, a case study for a realistic geometrical configuration is presented to explore the use of hard rough surfaces for reducing traffic noise in a tunnel which is constructed with hard boundaries.     

Experimental and numerical study on the propagation of impulsive sound around buildings

Propagation of impulsive sound around buildings and induced structural loading are investigated experimentally and numerically. Experiments were conducted on a rectangular building at Virginia Tech using sonic booms generated by shaped charges with an explosive weight of 0.78 kg, constructed from detonation cord. These experiments were simulated with a three-dimensional numerical model, in the context of geometrical acoustics (GA), by combining the image source method for the reflected field (specular reflections) with an extension of the Biot–Tolstoy–Medwin (BTM) method for the diffracted field. In this model, it is assumed that the acoustic propagation is linear and that all surfaces are acoustically rigid. This numerical model is validated against a boundary element (BE) solution and experimental data, showing a good overall agreement. The key advantages of this GA modeling approach for this application include the ability to model large three-dimensional domains over a wide frequency range and also to decompose the sound field into direct, reflected, and diffracted components, thus providing a better understanding of the sound-propagation mechanisms. Finally, this validated numerical model is used to investigate sound propagation around a cluster of six rectangular buildings, for a range of elevated source positions simulating sonic booms from aircraft.     

The attenuation of the higher-order cross-section modes in a duct with a thin porous layer

A numerical method for sound propagation of higher-order cross-sectional modes in a duct of arbitrary cross-section and boundary conditions with nonzero, complex acoustic admittance has been considered. This method assumes that the cross-section of the duct is uniform and that the duct is of a considerable length so that the longitudinal modes can be neglected. The problem is reduced to a two-dimensional (2D) finite element (FE) solution, from which a set of cross-sectional eigen-values and eigen-functions are determined. This result is used to obtain the modal frequencies, velocities and the attenuation coefficients. The 2D FE solution is then extended to three-dimensional via the normal mode decomposition technique. The numerical solution is validated against experimental data for sound propagation in a pipe with inner walls partially covered by coarse sand or granulated rubber. The values of the eigen-frequencies calculated from the proposed numerical model are validated against those predicted by the standard analytical solution for both a circular and rectangular pipe with rigid walls. It is shown that the considered numerical method is useful for predicting the sound pressure distribution, attenuation, and eigen-frequencies in a duct with acoustically nonrigid boundary conditions. The purpose of this work is to pave the way for the development of an efficient inverse problem solution for the remote characterization of the acoustic boundary conditions in natural and artificial waveguides.     

Low-frequency resonance of an oblate spheroidal cavity in a soft elastic medium

The horizontal ducting of sound by an oceanic temperature front over a sloping bottom is studied with an idealized wedge model consisting of a lateral interface across the slope. The water outside the frontal interface has higher temperature, hence faster sound speed, and it will produce inshore reflection/refraction of the sound. Combining the offshore refraction caused by the sloping bottom, propagating sound can be ducted along the front. An analytical solution to the sound pressure field in the idealized model is derived, and an example is presented to demonstrate and discuss the ducting effect.     

Calculation of low-frequency sound fields in irregular waveguides with strong backscattering

An approach is developed for calculating the sound fields in a non-stratified sea medium with irregularities that are not weak. The method of cross sections for horizontal parts of acoustic modes is used to obtain first-order causal equations that are equivalent to the boundary-value problem. A matrix equation describing the backscattered field of modes is analyzed, and the conditions that determine the weakness of the irregularities of the medium and the validity of the known approximate methods of sound field calculations are considered. The approximation of unidirectional propagation is represented in the form of quadratures. The example of a 2D shallow-water waveguide with a strongly irregular profile of a perfectly rigid bottom is considered to illustrate the advantages of the proposed approach in comparison with the approximate methods for specific low frequencies. The qualitative and quantitative differences that arise because of taking into account the backscattering between the curves of propagation losses corresponding to the exact solution and the conventional approximate methods are discussed.     

Dependence of the Mean Intensity of a Low-Frequency Acoustic Field on the Bottom Parameters of a Shallow Sea with Random Volumetric Water-Layer Inhomogeneities

The study is devoted to statistical modeling of low-frequency acoustic signal propagation in a twodimensionally inhomogeneous random shallow sea with a thermocline and differing penetrability of the bottom. Calculations are performed using the local-mode representation of the solution in the one-way propagation approximation. Plots are presented for the behavior of the mean acoustic field intensity for different sound velocity and density values in the bottom. It is shown that the earlier described effect of a decrease in propagation losses in a model randomly inhomogeneous shallow sea with an absorbing bottom significantly depends on the parameters of bottom sediments and is more strongly manifested for bottom boundaries with greater penetrability.     

Sound propagation in a duct with axial sound speed variation: An exact solution

The equation describing sound propagation in an ideal gas with exponential variation of static temperature in the direction of propagation is solved exactly in terms of known functions. Specific solutions for sound propagation in both infinite and semi-infinite length ducts with rigid walls are obtained. The alteration of the modal cut-off condition associated with an isothermal duct by the temperature variation is examined as well as the approach of other aspects of the solution to the familiar results for isothermal ducts. Comparison is also made with experimental data.     

On the conservation of momentum for a sound pulse reflecting from a pressure-release boundary

When a "massless" one-dimensional sound pulse (mass of a sound pulse is defined as an integral of the perturbation of density over the pulse length) reflects from a pressure-release boundary, its momentum changes sign. This obviously violates momentum conservation. However, in contrast to the case of an unbounded medium, calculation of the momentum in a bounded region includes a second-order term as well. Apparently, the second-order correction to the linear solution ensures momentum conservation in this case. The purpose of this Letter is to find a concrete form of this second-order correction. It appears that, as a result of the nonlinear interaction of the pulse with a pressure-release boundary, the latter experiences second-order net shift. This leads to the generation of a massive second-order rarefaction pulse whose momentum is directed opposite to the direction of propagation of the pulse itself. Appearance of this pulse ensures total momentum conservation.     

Sound Propagation in Shallow Water with an Inhomogeneous GAS-Saturated Bottom

We present the methods and results of numerical experiments studying the low-frequency sound propagation in one of the areas of the Arctic shelf with a randomly inhomogeneous gas-saturated bottom. The characteristics of the upper layer of bottom sedimentary rocks (sediments) used in calculations were obtained during a 3D seismic survey and trial drilling of the seafloor. We demonstrate the possibilities of substituting in numerical simulation a real bottom with a fluid homogeneous half-space where the effective value of the sound speed is equal to the average sound speed in the bottom, with averaging along the sound propagation path to a sediment depth of 0.6 wavelength in the bottom. An original technique is proposed for estimating the sound speed propagation in an upper inhomogeneous sediment layer. The technique is based on measurements of acoustic wave attenuation in water during waveguide propagation.     

Time-domain impedance formulation for transmission line matrix modelling of outdoor sound propagation

Outdoor sound propagation modelling has attracted considerable attention in the past and has lead to many analytical and numerical models. More recently, the increase of computational power has led to consider time-domain methods that enable to consider transient phenomena. Among these models, the transmission line matrix (TLM) method has been proposed, but the sound absorption at boundaries appears to be a somewhat underdeveloped aspect of this approach. In this paper, a specific implementation of impedance boundary condition is proposed. The method is based on the approximation of the impedance as a sum of linear systems, which allows the formulation of an equivalent impedance model in the time-domain. The proposed implementation is applied for two common impedance models of porous material. Numerical simulations have been carried out in the case of sound propagation over a flat ground with and without an impedance discontinuity, and for several values of specific airflow resistivity. TLM numerical predictions expressed in terms of excess attenuation relative to free field show a good agreement with analytical solutions.     

浅海涌浪对表面声道声传播的影响

受海面强风和海-气相互作用影响,表面声道普遍存在于冬季海洋环境中,是一种天然有利于声传播的波导.但是海面波浪使得海表形成粗糙界面,会严重破坏这种优良性能.本文利用南海北部海区的一次冬季声传播实验数据,研究表面声道声传播特性.研究表明,海底底质对表面声道内声传播的影响较弱,当海面风较小时,涌浪造成的影响为主要原因.实验数据显示,考虑涌浪后的粗糙海面给70km远处带来了10dB的传播损失增长.因此在考察南海北部海区冬季声场特性时,不仅要考虑海面风浪的影响,更需要考虑周围海域传来的涌浪的影响.研究涌浪存在时的声传播特性对提升声纳设备在海况较差时的使用性能具有重要意义.