Variations of mode amplitudes in a range-dependent waveguide

The ray method of calculating the mode amplitudes is used to analyze the sound fields in deep-water acoustic waveguides with two types of inhomogeneities of the refractive index: (i) weak inhomogeneities that cause small perturbations of ray trajectories and (ii) strong inhomogeneities with large spatial scales. Simple analytical relations are derived for describing the variations of the mode structure of the sound field in the presence of the aforementioned inhomogeneities. A new criterion defining the validity of the adiabatic approximation is formulated. To illustrate and test the results obtained, a numerical simulation of the sound fields is performed on the basis of the parabolic equation method.

     

Experimental investigation of an inversion technique for the determination of broadband duct mode amplitudes by the use of near-field sensor arrays

This paper is an experimental investigation of an inverse technique for deducing the amplitudes of the modes radiated from a turbofan engine, including schemes for stablizing the solution. The detection of broadband modes generated by a laboratory-scaled fan inlet is performed using a near-field array of microphones arranged in a geodesic geometry. This array geometry is shown to allow a robust and accurate modal inversion. The sound power radiated from the fan inlet and the coherence function between different modal amplitudes are also presented. The knowledge of such modal content is useful in helping to characterize the source mechanisms of fan broadband noise generation, for determining the most appropriate mode distribution model for duct liner predictions, and for making sound power measurements of the radiated sound field.     

Joint statistical moments of mode amplitudes at different frequencies in a random acoustic waveguide

This paper considers an approximate ray-based analytical approach for evaluating the joint statistical moments of mode amplitudes in an acoustic waveguide with large-scale sound speed fluctuations. Explicit analytic expressions for the statistical moments are derived from an approximate analytical solution of the mode-coupling equations. The analytic solution allows one to deduce a scaling law establishing the connection between amplitudes of modes with the same ratio of the mode number to frequency. The applicability of the ray-based approach for evaluating the joint statistical moments of modes amplitudes including the moments at different frequencies is demonstrated using the Monte Carlo simulation of sound fields in a model of the underwater acoustic waveguide in a deep ocean. Numerical simulation also shows different manifestations of the scaling law. In particular, it is shown how this law manifests itself in the acoustic energy distribution between normal modes, in the jump-like range variations of statistical moments, and in the shape of the correlation function between amplitudes of different modes at different frequencies.     

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.     

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.     

The horizontal structure of the sound field in the ocean

Results of calculating the horizontal structure of acoustic field in the ocean with a canonical sound velocity profile are presented. The calculation is performed in the framework of geometrical acoustics by combining the fields of water-path rays at every point with allowance for their phases and amplitudes. The field distribution at a fixed depth is found to be not very informative: within a cycle length, it contains 1–3 maxima, which are mainly caused by the caustics present at the given depth. The width of caustics is ～0.1–1 km. Between the caustics, as well as in their absence, the field amplitude is much smaller than that in the regions of caustics and varies depending on the phases and amplitudes of rays arriving at a given point. The comparison of the calculated horizontal field structure with that obtained from full-scale measurements for the regions between the caustics is difficult because of the possible fluctuations of sound propagation conditions.     

On the vertical structure of the sound field in a canonical waveguide at long ranges

The geometrical-acoustics approach is used to calculate the vertical structure of the sound field in an oceanic waveguide. The profile of the sound speed is specified to be canonical and range-independent along a 1000-km propagation path. A monochromatic sound source lies on the waveguide axis. It is shown that, at long distances from the source, the sound field formed by the water-path rays is mainly concentrated in the caustics, the number of which is determined by the number of the overlapping ray cycles at a given distance. A method for estimating the amplitude of the sound field produced by individual rays is proposed. The amplitudes obtained are used to calculate the total sound field along the vertical. A possible cause of the chaotic distribution of ray coordinates is considered. This cause may consist in the arbitrary choice of the number of rays and their departure angles without taking into account the discrete character of one of the variables. This mechanism of ray chaos formation furnishes an explanation for the fact that the chaos obtained in calculations is mainly associated with the flat rays.     

Acoustic coupling between the loudspeaker and the resonator in a standing-wave thermoacoustic device

Thermoacoustic refrigerators work with high amplitude sound waves, which are often created using an acoustic source coupled to a resonator. This coupling can be calculated analytically using linear acoustic equations and a linear model of the loudspeaker. This paper makes a comparison between such a coupling and measurements obtained in a large-scale thermoacoustic resonator constructed at the University of Manchester. The resonator was driven from low to large pressure amplitudes, with drive ratios up to 10%. It is shown that a good agreement is obtained for small amplitudes and this progressively worsens as the amplitude is increased. In the absence of wave harmonics and loudspeaker nonlinearities, the increasing discrepancy is attributed to the presence of minor losses.     

Optoacoustic conversion in suspensions: The competition of mechanisms and statistical characteristics

Optoacoustic conversion in diluted suspensions under the effect of nanosecond laser pulses is considered. The mode of operation with moderate values of the laser fluence is studied theoretically and experimentally. In this mode, a competition of the thermooptical and cavitation mechanisms of sound conversion is observed, which leads to considerable fluctuations of the acoustic response from one laser pulse to another. Analytical expressions for the basic characteristics of the acoustic signal are obtained. A simulation of the statistical characteristics of the cavitation contribution to the signal is performed using the Monte Carlo method. The experiment is based on the use of second harmonic pulses of a YAG laser and test suspensions. The histograms of the amplitudes of acoustic signals can be used to discriminate between the mechanisms of optoacoustic conversion and also can serve as the basis for diagnosing a low content of an insoluble phase in a liquid.     

激发圆形管道内多阶声模态的扬声器阵列控制方法

声模态发生器是通过控制扬声器阵列在管道内激发声模态波的一种装置。为了解决在管道内同时激发多个声模态的问题,研究了激发圆形管道内多阶声模态的扬声器阵列控制方法。采用轴向多圈布置的声源阵列,并调节各个声源的幅值和相位,实现同时激发包括径向声模态在内的多个声模态。同时考虑声源的周向位置和轴向位置信息,建立各个声源与多个目标模态系数之间的线性关系,运用最小二乘法求解得到激发目标多模态所需各个声源的复强度（包括幅值和相位）,所研制的高阶模态发生器以计算的声源复强度为输入量,采用数字信号系统控制扬声器输出的幅值和相位,用于实现管道内声源激发,该模态激发过程无需针对特定模态优化声源的位置。实验结果表明,所研制的模态发生器可精确激发单个或多个声模态,且目标模态系数信噪比几乎都大于10 dB。      

Wavelet packet based analysis of sound fields in rooms using coincident microphone arrays

This paper presents a passive analysis method for determining the spatio-temporal characteristics of sound fields in small rooms. The analysis finds an approximate directional reflectogram (ADR) which reveals the approximate arrival directions, time delays and amplitudes of the direct sound and early reflections without using a special or known sound source. A coincident microphone array is used to obtain directional recordings. The recordings are analysed by wavelet packet decomposition to determine the direction of the sound source and select wavelet packet coefficients to reconstruct the estimate of the direct sound. ADR is then computed via deconvolution using this estimate. Experiments have been carried out using synthesized recordings that were obtained from actual room impulse responses measured in two rooms for various source locations. The method estimates the source direction with a mean absolute error of about 7°. Calculated ADRs provide a good estimate of the time delays and arrival directions of acoustical reflections, whereas the amplitudes differ slightly.     

Effect of internal tides on slow energy fluctuations of impulse signals in an experiment on a long-distance stationary path

Temporal energy fluctuations of impuse signals generated by powerful explosive sources of sound are considered by using the experimental data obtained on a long-distance stationary path in the northwestern Pacific. The signals were received on the Kamchatka shelf (a characteristic ocean depth of about 200 m) at two points spaced by 115 km in the latitudinal direction, one of the reception points being located on the shelf far from its edge, and the other, on the shelf edge. The signal radiation was performed in the deep ocean, at a distance of about 1000 km from the shelf edge. Charges were exploded every hour for more than five days. The frequency-dependent energy fluctuations of the signals and those of the first mode alone were measured in the frequency range 10–80 Hz. It is shown that the amplitudes of energy fluctuations of the first mode in narrow bands can exceed 10 dB and make the main contribution to the energy fluctuations of the total signal. The maximum energy of the first mode is reached on the high tide. It is hypothesized that internal tide-induced variations of the sound velocity field on the shelf affect the degree of energy interaction between the first mode and the bottom.     

Virtual modes and the surface boundary condition in underwater acoustics

An explicit expression for the contribution of continuous normal modes to the acoustic pressure field in shallow water is derived under the assumption of constant sound speed in the bottom. An approximate evaluation of the resulting integral leads to a summation over “virtual” modes. These virtual modes are similar to the trapped modes except that their amplitudes decay with range. Their contribution is important in certain situations, for example at short ranges and where there may be few or no trapped modes. The validity of the “pressure release” boundary condition at the surface is investigated. This approximate boundary condition is justified by allowing for energy leakage into the air and examining the virtual mode contribution to the normal mode expression. These virtual modes converge identically to the usual trapped mode expression in the limit of zero air density.     

Mode competition in the orotron

A nonlinear, self-consistent and multimode analysis of the orotron is presented. The field in the cavity is expanded into the Hermite-Gaussian modes with time-dependent amplitudes, for which a set of ordinary differential equations is obtained from Maxwell's equations. The equations for the amplitudes are coupled to the equations of motion for the electrons. To yield a self-consistent solution, this set of coupled equations is solved simultaneously. The calculations yield transient and steady state behaviour, saturated efficiency, mode competition and multi-frequency behaviour.     

Acoustic phase conjugation in a three-phase medium

Acoustic phase conjugation is studied in a sandy marine sediment that contains air bubbles in its fluid fraction. The considered phase conjugation is a four-wave nonlinear parametric sound interaction caused by nonlinear bubble oscillations which are known to be dominant in acoustic nonlinear interactions in three-phase marine sediments. Two various mechanisms of phase conjugation are studied. One of them is based on the stimulated Raman-type sound scattering on resonance bubble oscillations. The other is associated with sound interactions with bubble oscillations whose frequencies are far from resonance bubble frequencies. Nonlinear equations to solve the phase conjugation problem are derived, expressions for acoustic wave amplitudes with a conjugate wave front are obtained and compared for various frequencies of the excited bubble oscillations.     

A rigorous study of the rf fields in complex cavities with gradual transitions

Based on mode coupling theory, the general form of coupled second order differential equations for the longitudinal rf standing-wave amplitudes in a complex cavity with gradual transition is developed. The TM type non-principal modes generated due to mode conversion are systematically taken into account. Comparisions of numerical results including or excluding TM modes are made for several examples and some interesting results are obtained.     

Sound attenuation in acoustically lined curved ducts in the absence of fluid flow

A study has been made of the sound attenuation in a lined curved duct with rectangular cross-section. In this study, the derivation of the eigenvalue equation was based on the continuity of the normal component of the particle displacement and the matching of the acoustic pressure on the acoustic lining surface. The sound attenuation was calculated by using the acoustic energy expression for the waves propagating in a curved duct. For a given duct geometry and known acoustic lining impedances, a computer program was developed to solve for the eigenvalues and to obtain the sound attenuation of the propagating waves in the lined curved duct. It was found that in the case studied here the fundamental mode was least attenuated. The total sound attenuation was calculated on the assumption that the amplitudes for all propagating waves were equal at a given frequency. Effects of aspect ratio, bend angle and the acoustic impedance on the sound attenuation were investigated in the present work.     

Sound source localization in an ocean waveguide

A robust algorithm for sound source localization in shallow sea based on a 2D Fourier transform of source motion interference patterns is developed. A spectrogram in time-frequency coordinates obtained after a Fourier transform contains localized areas of spectral density intensity of constructively interfering modes and a distributed area of noise spectral density. Signal spectral density is localized in an area whose linear sizes are determined by the lowest frequency and spatial scales of field variability. The peak input signal-to-noise ratio is estimated for a single receiver when robust detection is ensured and estimates of speed and initial distance to the receiver are close to the actual values. The high robustness of the algorithm is based on the coherent summation of mode amplitudes occurring at different times. Experimental results demonstrating the effectiveness of the algorithm are presented. For higher than peak signal-to-noise ratios, random estimates of the parameters are close to their statistically average values.     

Frequency shifts of sound field maxima under the effect of intense internal waves

Numerical simulation is carried out to study frequency shifts of a low-frequency sound field maxima under the effect of solitary internal waves (solitons) propagating along an acoustic track in the presence of mode coupling. The frequency shifts are measured by the correlation method. Simulation data obtained with allowance for mode coupling and data obtained in the adiabatic approximation are compared and analyzed.     

Multiple-order derivatives of a waveguide acoustic field with respect to sound speed, density, and frequency

An adjoint perturbative method is used to derive expressions for the first- through third-order derivatives of a pressure field with respect to sound speed, density, and frequency, for the restricted case of a laterally homogenous waveguide in which environmental parameters are only a function of depth. By using a normal-mode Green's function, the three-dimensional spatial correlation required by the standard acoustic adjoint equation can be reduced to a set of one-dimensional depth integrals. The resulting expressions for the first-order derivative are similar to those obtained by previous perturbative approaches based on the depth-separated wave equation, but the approach followed here permits straightforward extension to higher-order derivatives. Explicit evaluations of the expressions for a representative shallow-water waveguide model are in excellent agreement with numerical finite-difference computations. An analysis of the expressions as a function of source-receiver range finds the contributions to the mode amplitude derivatives to be non-negligible at ranges less than a few modal interference lengths, for parameters associated with the ocean bottom. Therefore, linear perturbative inversion methods that perturb only horizontal wavenumbers and not mode amplitudes should either be used with caution or modified to incorporate the expressions presented here.