Computed narrow-band time-reversing array retrofocusing in a dynamic shallow ocean

A time-reversing array (TRA) can retrofocus acoustic energy, in both time and space, to the original sound-source location without any environmental information. This unique capability may be degraded in time-dependent or noisy acoustic environments, or when propagation losses are prevalent. In this paper, monochromatic propagation simulations (based on the parabolic equation code, RAM) are used to predict TRA retrofocusing performance in shallow-water sound channels having characteristics similar to those measured during the recent SWARM (shallow-water acoustics in a random medium) experiment. Results for the influence of source-array range, source depth, acoustic frequency, bottom absorption, internal wave strength, and round-trip time delay are presented. For a fixed channel geometry, higher frequencies, deeper sources, and lower bottom absorption improve TRA performance and allow retrofocusing at longer ranges. In a dynamic shallow-water channel containing a random superposition of linear internal waves, the size of the retrofocus is slightly decreased and sidelobes are suppressed compared to the static channel results. These improvements last for approximately 1 to 2 min for source-array ranges near 10 km at a frequency of 500 Hz. For longer time delays, the internal waves cause significant TRA retrofocus amplitude decay, and the decay rate increases with increasing internal wave activity and acoustic frequency.     

Computed narrow-band azimuthal time-reversing array retrofocusing in shallow water.

The process of acoustic time reversal sends sound waves back to their point of origin in reciprocal acoustic environments even when the acoustic environment is unknown. The properties of the time-reversed field commonly depend on the frequency of the original signal, the characteristics of the acoustic environment, and the configuration of the time-reversing transducer array (TRA). In particular, vertical TRAs are predicted to produce horizontally confined foci in environments containing random volume refraction. This article validates and extends this prediction to shallow water environments via monochromatic Monte Carlo propagation simulations (based on parabolic equation computations using RAM). The computational results determine the azimuthal extent of a TRA's retrofocus in shallow-water sound channels either having random bottom roughness or containing random internal-wave-induced sound speed fluctuations. In both cases, randomness in the environment may reduce the predicted azimuthal angular width of the vertical TRA retrofocus to as little as several degrees (compared to 360 degrees for uniform environments) for source-array ranges from 5 to 20 km at frequencies from 500 Hz to 2 kHz. For both types of randomness, power law scalings are found to collapse the calculated azimuthal retrofocus widths for shallow sources over a variety of acoustic frequencies, source-array ranges, water column depths, and random fluctuation amplitudes and correlation scales. Comparisons are made between retrofocusing on shallow and deep sources, and in strongly and mildly absorbing environments.     

Observationally constrained modeling of sound in curved ocean internal waves: examination of deep ducting and surface ducting at short range

A study of 400 Hz sound focusing and ducting effects in a packet of curved nonlinear internal waves in shallow water is presented. Sound propagation roughly along the crests of the waves is simulated with a three-dimensional parabolic equation computational code, and the results are compared to measured propagation along fixed 3 and 6 km source/receiver paths. The measurements were made on the shelf of the South China Sea northeast of Tung-Sha Island. Construction of the time-varying three-dimensional sound-speed fields used in the modeling simulations was guided by environmental data collected concurrently with the acoustic data. Computed three-dimensional propagation results compare well with field observations. The simulations allow identification of time-dependent sound forward scattering and ducting processes within the curved internal gravity waves. Strong acoustic intensity enhancement was observed during passage of high-amplitude nonlinear waves over the source/receiver paths, and is replicated in the model. The waves were typical of the region (35 m vertical displacement). Two types of ducting are found in the model, which occur asynchronously. One type is three-dimensional modal trapping in deep ducts within the wave crests (shallow thermocline zones). The second type is surface ducting within the wave troughs (deep thermocline zones).     

南中国海海域存在孤立子内波条件下的 声场统计特性*

利用南海浅海海域低频声传播起伏实验中获取的水文数据,结合二维平流模型重构出声传播路径上的动态声速场,使用蒙特卡洛方法研究了有、无孤立子内波经过声传播路径条件下的声传播损失统计特性,并与实验结果进行了对比分析。仿真和实验结果表明：当孤立子内波经过声传播路径时,声传播损失起伏剧烈;与“下发上收”相比,“下发下收”情况下传播损失的概率分布更加分散。     

Predicting absorption and dispersion in acoustics by direct simulation Monte Carlo: Quantum and classical models for molecular relaxation

In the current study, real gas effects in the propagation of sound waves are simulated using the direct simulation Monte Carlo method for a wide range of frequencies. This particle method allows for treatment of acoustic phenomena at high Knudsen numbers, corresponding to low densities and a high ratio of the molecular mean free path to wavelength. Different methods to model the internal degrees of freedom of diatomic molecules and the exchange of translational, rotational and vibrational energies in collisions are employed in the current simulations of a diatomic gas. One of these methods is the fully classical rigid-rotor/harmonic-oscillator model for rotation and vibration. A second method takes into account the discrete quantum energy levels for vibration with the closely spaced rotational levels classically treated. This method gives a more realistic representation of the internal structure of diatomic and polyatomic molecules. Applications of these methods are investigated in diatomic nitrogen gas in order to study the propagation of sound and its attenuation and dispersion along with their dependence on temperature. With the direct simulation method, significant deviations from continuum predictions are also observed for high Knudsen number flows.     

深远海线性内波条件下声场时间相关性的空间分布

深海声场特定的干涉结构导致其时间相关性的空间起伏,研究这种空间特性可以为水声信号的探测与处理提供重要参考。利用抛物方程声场仿真模型,联合Monte-Carlo数值方法计算分析了深远海线性内波条件下声场时间相关性的空间分布特性。与现有的研究相比,给出了时间相关性的距离和深度起伏特征。结果表明,当接收达到一定距离,声场时间相关性的空间分布具有与声场干涉条纹类似的结构,声场干涉越强,时间相关性越好。此外,声源频率和声速标准差的变化会引起时间相关性空间分布规律的改变,且会聚区传播模式下的改变强于深海声道传播模式。      

The coherence of low-frequency sound in shallow water in the presence of internal waves

The coherence time and transverse coherence length of a low-frequency (100–300 Hz) sound field that is formed by an omnidirectional point source at a distance of 10–30 km in a shallow-water acoustic waveguide, which is characteristic of an open ocean shelf, were estimated analytically and in a numerical experiment. An anisotropic field of background internal waves is considered as a source of spatiotemporal fluctuations. It is shown that the coherence time decreases as the frequency increases, and strongly depends on the perturbation-movement direction. The transverse coherence length is primarily determined by phase incursions that are related to the cylindrical shape of the acoustic-wave front. In the case of transverse propagation, background internal waves may lead to significant variations in this length. The introduction of compensating phase corrections during processing provides a considerable increase in the average transverse coherence length.     

Features of the energy structure of acoustic fields in the ocean with two-dimensional random inhomogeneities

The paper is devoted to the analytic study and numerical simulation of mid-frequency acoustic signal propagation in a two-dimensional inhomogeneous random shallow-water medium. The study was carried out by the cross section method (local modes). We present original theoretical estimates for the behavior of the average acoustic field intensity and show that at different distances, the features of propagation loss behavior are determined by the intensity of fluctuations and their horizontal scale and depend on the initial regular parameters, such as the emission frequency and size of sound losses in the bottom. We establish analytically that for the considered waveguide and sound frequency parameters, mode coupling effect has a local character and weakly influences the statistics. We establish that the specific form of the spatial spectrum of sound velocity inhomogeneities for the statistical patterns of the field intensity is insignificant during observations in the range of shallow-water distances of practical interest.     

Phase fluctuations of focused low-frequency sound fields in shallow water

Numerical experiments are carried out to study the phase fluctuations of a focused low-frequency sound field on an oceanic shelf. The focusing of sound at a distance of several kilometers is simulated using the phase conjugation of sound waves. Perturbations of the medium are represented by high-frequency (>1 cph) background internal waves and by the wind waves on the ocean surface. It is shown that, for a focused sound field at frequencies of several hundreds of hertz, the phase fluctuations do not exceed π and can be measured against the background of acoustic noise typical of shallow-water regions of the ocean. The fluctuation magnitude can be reduced approximately by half through the optimal choice of the mode composition. In the presence of such fluctuations, it is possible to measure the relative variations of the length of a stationary acoustic path with an accuracy of 1 m or better at a wind speed no greater than 10 m/s and a typical intensity of background internal waves.     

Pulse propagation of acoustic waves scattered in a channel

When acoustic waves are scattered by random sound-speed fluctuations in a two-dimensional channel the energy is continually transferred between the propagating modes. In the multiple- scattering region the energy flux assumes an asymptotic form in which there is equal energy flux propagating in each mode. Here we shall make use of this well known result to show how to obtain an asymptotic form for a pulse of acoustic energy propagating in the channel. In the multiple-scattering region the speed of the acoustic waves in the pulse continually changes as the energy is transferred between the modes. The process is basically a diffusion process around the mean speed of propagation. We shall first show, using physical arguments, that the diffusion coefficient is proportional to the square root of the propagation distance times the mean free path of scattering. The theory governing the acoustic propagation in the channel is formulated in terms of modal coherence equations and we shall next give a brief review of the definitions of the coherence functions and a discussion of how the equations governing the propagation of the modal coherence functions are derived. We shall then show how the pulse shape and the relevant parameters may be obtained by solving the basic modal coherence equations at large propagation distances.     

Temporal coherence of acoustic signals in a fluctuating ocean

Temporal coherence of acoustic signals propagating in a fluctuating ocean is important for many practical applications and has been studied intensively experimentally. However, only a few theoretical formulations of temporal coherence exist. In the present paper, a three-dimensional (3D) modal theory of sound propagation in a fluctuating ocean is used to derive closed-form equations for the spatial-temporal coherence function of a broadband signal. The theory is applied to the analysis of the temporal coherence of a monochromatic signal propagating in an ocean perturbed by linear internal waves obeying the Garrett-Munk (G-M) spectral model. In particular, the temporal coherence function is calculated for propagation ranges up to 10(4) km and for five sound frequencies: 12, 25, 50, 75, and 100 Hz. Then, the dependence of the coherence time (i.e., the value of the time lag at which the temporal coherence decreases by a factor of e) on range and frequency is studied. The results obtained are compared with experimental data and predictions of the path-integral theory.     

3/2omega0 radiation from the laser-driven two-plasmon decay instability in an inhomogeneous plasma

We present the results of the first reduced model simulations of the nonlinear development of the two-plasmon decay instability in an inhomogeneous plasma, including properties of the 3/2 harmonic emission. A sharp increase in radiation and Langmuir turbulence fluctuation levels occurs above a threshold laser intensity that depends on initial fluctuation levels. We study the competition between the linear propagation of Langmuir waves in the density gradient and the nonlinear saturation due to the Langmuir decay instability. The secondary decay Langmuir waves can provide the dominant source of the radiation and are essential to explain experiments.     

Effects of wind waves on horizontal array performance in shallow-water conditions

We analyze the influence of statistical effects of the propagation of an acoustic signal excited by a tone source in a shallow-water channel with a rough sea surface on the efficiency of a horizontal phased array. As the array characteristics, we consider the angular function of the array response for a given direction to the source and the coefficient of amplification of the signal-to-noise ratio (array gain). Numerical simulation was conducted in to the winter hydrological conditions of the Barents Sea in a wide range of parameters determining the spatial signal coherence. The results show the main physical effects of the influence of wind waves on the array characteristics and make it possible to quantitatively predict the efficiency of a large horizontal array in realistic shallow-water channels.     

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.     

Acoustic propagation through anisotropic internal wave fields: transmission loss, cross-range coherence, and horizontal refraction

Results of a computer simulation study are presented for acoustic propagation in a shallow water, anisotropic ocean environment. The water column is characterized by random volume fluctuations in the sound speed field that are induced by internal gravity waves, and this variability is superimposed on a dominant summer thermocline. Both the internal wave field and resulting sound speed perturbations are represented in three-dimensional (3D) space and evolve in time. The isopycnal displacements consist of two components: a spatially diffuse, horizontally isotropic component and a spatially localized contribution from an undular bore (i.e., a solitary wave packet or solibore) that exhibits horizontal (azimuthal) anisotropy. An acoustic field is propagated through this waveguide using a 3D parabolic equation code based on differential operators representing wide-angle coverage in elevation and narrow-angle coverage in azimuth. Transmission loss is evaluated both for fixed time snapshots of the environment and as a function of time over an ordered set of snapshots which represent the time-evolving sound speed distribution. Horizontal acoustic coherence, also known as transverse or cross-range coherence, is estimated for horizontally separated points in the direction normal to the source-receiver orientation. Both transmission loss and spatial coherence are computed at acoustic frequencies 200 and 400 Hz for ranges extending to 10 km, a cross-range of 1 km, and a water depth of 68 m. Azimuthal filtering of the propagated field occurs for this environment, with the strongest variations appearing when propagation is parallel to the solitary wave depressions of the thermocline. A large anisotropic degradation in horizontal coherence occurs under the same conditions. Horizontal refraction of the acoustic wave front is responsible for the degradation, as demonstrated by an energy gradient analysis of in-plane and out-of-plane energy transfer. The solitary wave packet is interpreted as a nonstationary oceanographic waveguide within the water column, preferentially funneling acoustic energy between the thermocline depressions.     

Temporal coherence of acoustic rays and modes using the path integral approach

Acoustic propagation can be described by rays and normal modes. Applying the path integral to refractive rays in three dimensional space, Dashen et al. [J. Acoust. Soc. Am. 77, 1716-1722 (1985)] derived the mutual coherence function of the acoustic field. For shallow water where sound interacts with boundaries, the acoustic field can be described by vertical modes and horizontal rays. Applying the path integral to the horizontal rays, one obtains the mutual coherence function of the normal modes. This paper applies this formulation to the derivation of the temporal coherence function of individual modes and also that of the acoustic field in the presence of linear internal waves. The effects of mode coupling due to internal waves on temporal coherence loss are illustrated with numerical calculations.     

Analytical and numerical prediction of harmonic sound power in the inlet of aero-engines with emphasis on transonic rotation speeds

Tone noise radiated through the inlet of a turbofan is mainly due to rotor-stator interactions at subsonic regimes (approach flight), and to the shock waves attached to each blade at supersonic helical tip speeds (takeoff). The axial compressor of a helicopter turboshaft engine is transonic as well and can be studied like turbofans at takeoff. The objective of the paper is to predict the sound power at the inlet radiating into the free field, with a focus on transonic conditions because sound levels are much higher. Direct numerical computation of tone acoustic power is based on a RANS (Reynolds averaged Navier–Stokes) solver followed by an integration of acoustic intensity over specified inlet cross-sections, derived from Cantrell and Hart equations (valid in irrotational flows). In transonic regimes, sound power decreases along the intake because of nonlinear propagation, which must be discriminated from numerical dissipation. This is one of the reasons why an analytical approach is also suggested. It is based on three steps: (i) appraisal of the initial pressure jump of the shock waves; (ii) 2D nonlinear propagation model of Morfey and Fisher; (iii) calculation of the sound power of the 3D ducted acoustic field. In this model, all the blades are assumed to be identical such that only the blade passing frequency and its harmonics are predicted (like in the present numerical simulations). However, transfer from blade passing frequency to multiple pure tones can be evaluated in a fourth step through a statistical analysis of irregularities between blades. Interest of the analytical method is to provide a good estimate of nonlinear acoustic propagation in the upstream duct while being easy and fast to compute. The various methods are applied to two turbofan models, respectively in approach (subsonic) and takeoff (transonic) conditions, and to a Turbomeca turboshaft engine (transonic case). The analytical method in transonic appears to be quite reliable by comparison with the numerical solution and with available experimental data.     

Characteristics and application of laser-generated acoustic shock waves in air

When a high-power laser beam is focused at a point, the air at the focal point is heated to temperatures of thousands of degrees within several nanoseconds and breaks down. This generates a spark that, in turn, is accompanied by an acoustic shock wave. The acoustic shock waves generated by focussing the beam from a pulsed laser with a 1064 nm wavelength and a power of 800 mJ per pulse have been measured using 1/4″ and 1/8″ B&K microphones. Nonlinear sound levels are observed up to 1.5 m from the laser-induced sparks. Beyond a certain region close to the source, levels are found to decrease in a manner consistent with spherical spreading plus nonlinear hydrodynamic losses. Analysis of the waveforms shows that the acoustic pulses associated with the laser-induced sparks are more repeatable and have higher intensity than those from an electrical spark source. Laser-generated acoustic shock waves are ideal for simulating a blast wave or a sonic boom in the laboratory and for studying the associated propagation effects. To illustrate this application, the propagation of the laser generated shock waves over a series of different hard, rough surfaces has been investigated. The results show the distinctive influences of ground roughness on the propagation of the shock wave.     

非线性波动方程的新数值迭代方法

提出了一种新的求解非线性波动方程的数值迭代法,它是一种半解析的方法.与完全的数值计算方法扰法相比,它能够考虑各阶谐波的相互作用,且能够满足能量守恒定律.用它研究了非线性声波在液体中的传播性质,结果表明,在微扰法适用的声强范围内迭代法也适用,在微扰法不适用的一个较宽的声强范围内迭代法依然适用.     

Study of a novel range-dependent propagation effect with application to the axial injection of signals from the Kaneohe source

A novel range-dependent propagation effect occurs when a source is placed on the seafloor in shallow water with a downward refracting sound speed profile, and sound waves propagate down a slope into deep water. Under these conditions, small grazing-angle sound waves slide along the bottom downward and outward from the source until they reach the depth of the sound channel axis in deep water, where they are detached from the sloping bottom and continue to propagate outward near the sound channel axis. This "mudslide" effect is one of a few robust and predictable acoustic propagation effects that occur in range-dependent ocean environments. As a consequence of this effect, a bottom mounted source in shallow water can inject a significant amount of acoustic energy into the axis of the deep ocean sound channel that can then propagate to very long ranges. Numerical simulations with a full-wave range-dependent acoustic model show that the Kaneohe experiment had the appropriate source, bathymetry, and sound speed profiles that allows this effect to operate efficiently. This supports the interpretation that some of the near-axial acoustic signals, received near the coast of California from the bottom mounted source located in shallow water in Kaneohe Bay, Oahu, Hawaii, were injected into the sound channel of the deep Pacific Ocean by this mechanism. Numerical simulations suggest that the mudslide effect is robust.