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.     

Range dependence of the vertical structure of the sound field in the ocean

In the ocean without fluctuations, the sound field is calculated by the method of geometrical acoustics with allowance for purely water-path rays in a sound channel of canonical shape with a thickness of 4 km for distances of 500 and 2000 km. The sound field is determined as a sum of individual rays arriving at a given point with their own amplitudes and phases. It is shown that the vertical structure of the sound field consists of a number of caustics separated by regions with a quasi-random distribution of the field whose amplitude is much smaller than that in the caustics. At a fixed distance, the number of caustics is equal to the difference between the numbers of the ray turning points at the boundaries of the departure angle range. As the distance from the source increases, the number of caustics increases proportionally to distance.     

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.     

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.     

Slowness surfaces, ray velocity surfaces and phonon focussing in highT c superconductor crystals

This paper reports the results of the study of anisotropy in elastic wave propagation in single crystal superconducting BSCCO. The inverse and group velocities of elastic waves propagating in different directions have been computed and the corresponding slowness and ray velocity surfaces plotted, taking elastic constant data from literature. In addition, the phenomenon of phonon focussing has been investigated in this material by computing the phonon enhancement factor along different directions in spherical polar coordinates. The abnormally high values in phonon enhancement factor exhibited in certain directions for the phonon modes are interpreted as due to caustics occurring in the geometrical acoustics approximation adopted in the computational analysis. The results in LSCO and YBCO are found to be similar to those in BSCCO.     

The Ray-Wave correspondence and the suppression of chaos in long-range sound propagation in the ocean

The long-range sound propagation in a horizontally inhomogeneous underwater sound channel is considered. It is shown that the vertical oscillations of inhomogeneity affect the near-axis rays in a resonant way and destroy their stability. As a consequence, the near-axis rays exhibit a chaotic behavior. The ray chaos manifests itself as intensification of interaction between adjacent low-order modes. In this case, a great number of strongly coupled modes appear, and the field structure near the channel axis becomes diffusive. However, as the signal frequency decreases, the inhomogeneity oscillations in depth lead to decoupling of adjacent modes and, hence, to suppression of chaos. As a result, the field structure near the channel axis becomes regular, which is confirmed by numerical simulation.     

Parallel optimization of underwater acoustic models: A survey

Underwater acoustic models are effective tools for simulating underwater sound propagation. More than 50 years of research have been conducted on the theory and computational models of sound propagation in the ocean. Unfortunately, underwater sound propagation models were unable to solve practical large-scale three-dimensional problems for many years due to limited computing power and hardware conditions. Since the mid-1980s, research on high performance computing for acoustic propagation models in the field of underwater acoustics has flourished with the emergence of high-performance computing platforms, enabling underwater acoustic propagation models to solve many practical application problems that could not be solved before. In this paper, the contributions of research on high-performance computing for underwater acoustic propagation models since the 1980s are thoroughly reviewed and the possible development directions for the future are outlined.     

An effective quiescent medium for sound propagating through an inhomogeneous,moving fluid

The idea of similarity between acoustic fields in a moving fluid and in a certain "effective" quiescent medium, first put forward by Lord Rayleigh, proved very helpful in understanding and modeling sound propagation in an atmosphere with winds and in an ocean with currents, as well as in other applications involving flows with small velocity compared to sound speed. Known as effective sound speed approximation, the idea is routinely utilized in the contexts of the ray theory, normal mode representation of the sound field, and the parabolic approximation. Despite the wide use of the concept of effective sound speed in acoustics of moving media, no theoretical justification of Rayleigh's idea was published that would be independent of the chosen representation of the sound field and uniformly apply to distinct propagation regimes. In this paper, we present such a justification by reducing boundary conditions and a wave equation governing sound fields in the inhomogeneous moving fluid with a slow flow to boundary conditions and a wave equation in a quiescent fluid with effective sound speed and density. The derivation provides insight into validity conditions of the concept of effective quiescent fluid. Introduction of effective density in conjunction with effective sound speed is essential to ensure accurate reproduction of acoustic pressure amplitude in the effective medium. Effective parameters depend on sound speed, flow velocity, and density of the moving fluid as well as on sound propagation direction. Conditions are discussed under which the dependence on the propagation direction can be avoided or relaxed.     

Weakly divergent ray and diffraction beams in oceanic waveguides

Conditions that should be satisfied by the sound velocity profile of an oceanic waveguide for the dependence of the ray cycle length on the ray phase velocity to contain smooth extrema are formulated. The extrema correspond to weakly divergent ray beams forming “caustic” beams. It is found that diffraction effects cause a considerable smoothing of the sharp extrema that occur in the dependence of the interference period of neighboring modes on their phase velocity. As a result, in addition to the weakly divergent ray beams, weakly divergent diffraction beams and the corresponding “diffraction” caustics can be formed.     

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.     

Parabolic equation for nonlinear acoustic wave propagation in inhomogeneous moving media

A new parabolic equation is derived to describe the propagation of nonlinear sound waves in inhomogeneous moving media. The equation accounts for diffraction, nonlinearity, absorption, scalar inhomogeneities (density and sound speed), and vectorial inhomogeneities (flow). A numerical algorithm employed earlier to solve the KZK equation is adapted to this more general case. A two-dimensional version of the algorithm is used to investigate the propagation of nonlinear periodic waves in media with random inhomogeneities. For the case of scalar inhomogeneities, including the case of a flow parallel to the wave propagation direction, a complex acoustic field structure with multiple caustics is obtained. Inclusion of the transverse component of vectorial random inhomogeneities has little effect on the acoustic field. However, when a uniform transverse flow is present, the field structure is shifted without changing its morphology. The impact of nonlinearity is twofold: it produces strong shock waves in focal regions, while, outside the caustics, it produces higher harmonics without any shocks. When the intensity is averaged across the beam propagating through a random medium, it evolves similarly to the intensity of a plane nonlinear wave, indicating that the transverse redistribution of acoustic energy gives no considerable contribution to nonlinear absorption. Published in Russian in Akusticheskiĭ Zhurnal, 2006, Vol. 52, No. 6, pp. 725–735. This article was translated by the authors.     

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.     

On the acoustic modes in a cylindrical duct with an arbitrary wall impedance distribution

The present paper considers the propagation of sound in a cylindrical duct, with a wall section of finite length covered by an acoustic liner whose impedance is an arbitrary function of position. The cases of (i) uniform wall impedance, and wall impedance varying along the (ii) circumference or (iii) axis of the duct, or (iv) both simultaneously, are explicitly considered. It is shown that a nonuniform wall impedance couples modes with distinct azimuthal l or axial m wave numbers, so that their radial wave numbers k can no longer be calculated separately for each pair (m,l). The radial wave numbers are the roots of an infinite determinant, in the case when the wall impedance varies either (i) circumferentially or (ii) radially. If the wall impedance varies (iv) both radially and circumferentially, then the radial wave numbers are the roots of a doubly infinite determinant, i.e., an infinite determinant in which each term is an infinite determinant. The infinite determinants specifying the radial wave numbers are written explicitly for sound in a cylindrical nozzle with a uniform axial flow, in which case the radial eigenfunctions are Bessel functions; the method of calculation of the radial wave numbers applies equally well to a cylindrical nozzle with shear flow and/or swirling flows, with the Bessel functions replaced by other eigenfunctions. The radial wave numbers are calculated by truncation of the infinite determinants, for several values of the aspect ratio, defined as the ratio of length to diameter. It is shown that a nonuniform wall impedance will give rise to additional modes compared with a uniform wall impedance. The radial wave numbers specify the eigenfrequencies for the acoustic modes in the duct; the imaginary parts of the eigenfrequencies specify the decay of the sound field with time, and thus the effectiveness of the acoustic liner.     

Acoustic radiation from a shell-encapsulated baffled cylindrical cap

An exact study of radiation of an acoustic field due to radial/axial vibrations of a baffled cylindrical piston, eccentrically positioned within a fluid-filled thin cylindrical elastic shell, into an external fluid medium is presented. This configuration, which is a realistic idealization of a liquid-filled cylindrical acoustic lens with a focal point inside the lens when used as a sound projector, is of practical importance with a multitude of possible applications in underwater acoustics and ocean engineering. The formulation utilizes the appropriate wave field expansions along with the translational addition theorems for cylindrical wave functions to develop a closed-form solution in the form of an infinite series. Numerical results reveal the key effects of excitation frequency, cap angle, radiator position (eccentricity), dynamics of the elastic shell, and cap surface velocity distribution on sound radiation.     

水下声学滑翔机用于东印度洋声传播特性分析及声源估计

常规实验方法无法同步获取深海大尺度声学和水文数据,水下滑翔机可作为同步观测平台解决该问题.首先利用在东印度洋北部海域水下滑翔机同步获取的声传播和水文实验数据,分析了水下滑翔机的自噪声谱级和实验海区声传播特性,然后推算并修正了滑翔机水下运动轨迹,利用第一影区水下滑翔机接收声传播信号的脉冲多途到达时间差对声源进行测距与定深。潜标接收噪声与滑翔机自噪声谱级对比表明,水下滑翔机在海洋中无动力运动时的系统自噪声接近于潜标观测的海洋环境噪声。滑翔机实测的声传播损失与模型计算结果吻合较好,第一影区水下声源测距定深结果与实际位置较为一致,测距与定深的相对误差均小于5%。利用加载水听器的水下滑翔机可以实现水文环境数据与声学信号的同步观测,对深海声传播特性测量及定位算法研究具有重要意义。      

Space-time and frequency-phase stability of the acoustic field in the underwater sound channel

The space-time and frequency-phase stability of the acoustic field is studied for the case of long-range propagation in the underwater sound channel. The possibility of splitting the field components produced by the Doppler effect in the total interference structure of a monochromatic signal is revealed for different ranges, parameters of the channel inhomogeneities, and frequencies. The experiments are performed in summertime in the northwestern part of the Pacific Ocean, near the Kamchatka Peninsula, on a path of 2100 km. Highly stable sound sources with resonant frequencies of 230 and 380 Hz are used for the measurements. The sources are towed at a depth of 70 m with a speed of 5–6 knots. To receive the signal near the channel axis, a bottom-moored (at a depth of 200 m) stationary system is used. The width of the sound beams is studied, and the broadening limits of the frequency spectra are estimated for the coherent and incoherent field components in the case of super-long-range sound propagation. The phase velocities of the split components are determined.     

三维复杂温度场高精度声学测量方法

声学温度场检测技术通过多路径声波传播时间数据,反演被测区域的温度分布.提供了一种高精度的三维复杂温度场的声学测量方法.首先从射线声学角度给出了三维非均匀温度场中声波传播路径的数学模型.在此基础上,将三维温度场的重建问题转化为声波传播路径的求解和温度场的反演问题,建立了基于多项式修正径向基函数(RBF-PR)和改进的Ti...     

深海不完整声道下反转点会聚区研究

近期南海远程声传播实验数据的处理分析表明在深海不完整声道中声道轴以下存在一种会聚区,该会聚区相比于海面附近的上反转点会聚区在远距离处具有更高的会聚增益.本文利用射线简正波理论确定了水中反转型焦散线和海面反射型焦散线位置,对比发现实验中观测到的深海大深度会聚区位置与水中反转型焦散线位置一致,证明该会聚区是由大量简正波同相...