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。      

Horizontal refraction of sound rays due to short-period internal waves in the ocean

The effect of a short-period internal wave measured in field conditions on the horizontal (side) refraction of sound rays is estimated. The angle of horizontal refraction, i.e., the angle between the direction of the signal arrival in the horizontal plane and the true direction to the sound source, is determined. The influence of various factors, such as the position of the receiving system in depth with respect to the layer of high sound velocity gradients, the rotation of the transmitter-receiver track with respect to the internal wave front, etc., on the horizontal refraction is estimated. Numerical calculations are carried out. Conclusions about the possible errors that arise in determining the azimuth direction to the sound source because of the effect of short-period internal waves are derived.     

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.     

Restless rays, steady wave fronts

Observations of underwater acoustic fields with vertical line arrays and numerical simulations of long-range sound propagation in an ocean perturbed by internal gravity waves indicate that acoustic wave fronts are much more stable than the rays comprising these wave fronts. This paper provides a theoretical explanation of the phenomenon of wave front stability in a medium with weak sound-speed perturbations. It is shown analytically that at propagation ranges that are large compared to the correlation length of the sound-speed perturbations but smaller than ranges at which ray chaos develops, end points of rays launched from a point source and having a given travel time are scattered primarily along the wave front corresponding to the same travel time in the unperturbed environment. The ratio of root mean square displacements of the ray end points along and across the unperturbed wave front increases with range as the ratio of ray length to correlation length of environmental perturbations. An intuitive physical explanation of the theoretical results is proposed. The relative stability of wave fronts compared to rays is shown to follow from Fermat's principle and dimensional considerations.     

Sound field phase front variations in shallow water in the presence of intense internal waves

The method of vertical modes and horizontal rays and the method of parabolic equation in the horizontal plane are used to study space-time fluctuations of the phase front of the sound field in the presence of a train of internal waves passing through the acoustic path. The possibility of measuring the distortions of the phase front with a simultaneous filtering of modes by a horizontal array is analyzed. A numerical simulation is carried out for the conditions corresponding to the Eastern coast of United States and the Barents Sea.     

Frequency dependence and intensity fluctuations due to shallow water internal waves

A theory and experimental results for sound propagation through an anisotropic shallow water environment are presented to examine the frequency dependence of the scintillation index in the presence of internal waves. The theory of horizontal rays and vertical modes is used to establish the azimutal and frequency behavior of the sound intensity fluctuations, specifically for shallow water broadband acoustic signals propagating through internal waves. This theory is then used to examine the frequency dependent, anisotropic acoustic field measured during the SWARM'95 experiment. The frequency dependent modal scintillation index is described for the frequency range of 30-200 Hz on the New Jersey continental shelf.     

Internal wave effects on the ambient noise notch in the East China Sea: model/data comparison

The vertical directivity pattern of the ambient noise field observed in shallow water is typically anisotropic with a trough in the horizontal. This trough, often called the ambient noise notch, develops because downward refraction steepens all rays emanating from near the sea surface. Variability in the environment has the potential to redistribute the noise into shallower angles and thereby fill the notch. In the present work, a model for the width and depth of the ambient noise notch is developed. Transport theory for acoustic propagation is combined with a shallow water internal wave model to predict the average output of a beamformer. Ambient noise data from the East China Sea are analyzed in the 1-to-5-kHz band. Good agreement between the model and the data for both the width and depth of the ambient noise notch is obtained at multiple frequencies, suggesting that internal wave effects are significant.     

南海北部海域内波环境下声传播损失起伏统计特性

浅海内波会引起声传播能量随时间的起伏变化,进而影响水声设备的工作性能.本文利用2015年南海北部一次浅海声场起伏实验数据,对比分析了浅海线性内波和孤立子内波条件下的声传播损失统计特性.在孤立子内波条件下,声传播损失起伏明显加剧,可达11 dB,且分布明显展宽,相对于线性内波的环境,声传播损失起伏可增加5 dB.从简正波...     

Characteristic features of the sound field formation near the bottom of a shallow sea

Detailed calculated data are presented for the angular, temporal, and energy structures of the sound field at the points of localtion of a horizontal line array of receivers (at 250-m intervals) in a shallow sea. The array is deployed near the bottom of a 200-m-deep waveguide along a sound propagation track, at distances from 20 to 30 km from a source generating a signal in the kilohertz frequency range. The influence of a sand or mud bottom on the intensity of signals arriving along single rays is numerically estimated for winter and summer conditions of sound propagation in a specific region of the Barents Sea.     

Frequency shifts of the sound field interference pattern in shallow water because of second-mode soliton-like internal waves

Numerical simulation is carried out to analyze the effect of an internal soliton of the second gravity mode on low-frequency sound propagation in an oceanic shelf region. The simulation is performed using the data of a full-scale experiment performed on the shelf of the South China Sea near Dongsha atoll, where the aforementioned solitons had been detected by stationary vertical thermistor arrays. The calculations take into account the effect of horizontal refraction of sound waves. It is assumed that a stationary acoustic track is oriented across the predominant propagation direction of internal waves. The results of simulation show that, when the soliton crosses the stationary track, some of the sound field modes are focused, whereas other modes are defocused. It is demonstrated that the soliton parameters can be adequately determined from the frequency shifts of the sound field interference pattern. However, such an estimate of the soliton parameters is only possible for a limited length of the stationary track for which the effect of horizontal refraction is sufficiently weak.     

Rearrangement of the horizontal space-time structure of the sound field in shallow water in the presence of moving internal waves

The rearrangement of the space-time structure of the sound field in a shallow-water waveguide with a moving intense internal wave packet is considered. The analysis is performed in terms of an approach characterized by space-time horizontal rays and vertical modes. It is shown that, within the time the packet travels over the acoustic track (about an hour), considerable spatial and temporal fluctuations occur in the field intensity and interference structure.     

Experimental and theoretical study of the vertical coherence of the sound field in a shallow sea

The combined effect of multiple scattering by random inhomogeneities of a waveguide and bottomcaused sound absorption is known to be a fundamental factor that governs the formation of the sound field in a shallow sea [1, 2]. A number of publications [2–6] present statistical analyses of the fluctuation phenomena that accompany the sound propagation in shallow sea regions. In these publications, most attention is paid to studying the evolution of the intensities of normal waves under the effect of scattering by the random field of internal waves. It is shown that in natural conditions, in addition to the inhomogeneities of the water column, one should take into account the irregular boundaries of the sound channel, which can also affect the correlation characteristics of the sound field. In this paper, we present experimental data on the vertical coherence of the sound field on a fixed path in the Barents Sea. We also compare the experimental data with theoretical calculations based on a model of sound scattering by the rough sea surface.     

南海深海典型不平整地形对声场垂直相关性的影响

海底地形变化对深海环境下的声传播和空间相关性有重要影响。基于2014年南海中南部海域不完全深海声道条件下大跨度垂直阵接收的声信号,选取平坦海底和典型不平整(存在小海底山和海底斜坡)海底两个不同传播方向上传播损失差异较大的距离,对声场垂直相关性进行了对比分析,并应用射线理论对相关性差异予以定性分析和机理解释。在不平整海底方向,在第一影区内小海底山遮挡区附近:在部分一次海底反射声线被小海底山遮挡的距离处,接收声信号主脉冲多途干涉结构相对平坦海底方向更加简单,垂直相关性增强;而在全部一次海底反射声线被小海底山遮挡的距离处,对声场起主要作用的变为二次海底反射声线,接收声信号主脉冲呈现多途干涉结构,垂直相关性降低。在第一会聚区附近:平坦海底环境下,由于两组水体中反转声线在空间垂直方向上的干涉效应,使得声场的垂直相关随接收深度增加呈现出周期性振荡的现象;而不平整海底方向,在50 km处,海底斜坡阻挡了一组水体反转声线,在大深度上只出现单会聚结构,观测不到垂直相关的周期性振荡现象;在57 km附近对声场起主要贡献的成分从水体中反转声线变成了多次海底反射声线,主脉冲多途展宽变宽,垂直相关性显著降低。研究结果对深海复杂海底地形环境下声场垂直相关性的深入分析及声呐阵列增益估计等具有重要意义。      

Noise field anisotropy of surface sources in a coastal region with arbitrary bottom relief and sound velocity profile

The noise field anisotropy of surface sources in a coastal region with an arbitrary three-dimensional bottom relief and an arbitrary sound velocity profile is investigated. The results of computations performed by a computer code in two stages are presented. The first stage consists in the computation of horizontal rays, i.e., the projections of the real rays multiply reflected from the bottom and sea surface onto the horizontal plane. The second stage summarizes the contributions of the noise sources lying within the surface elements that are cut out on the sea surface by a narrow ray tube launched from the point of observation in a given direction. The computations show that, in the coastal region, the noise field is essentially anisotropic, and this anisotropy occurs not only in the vertical plane, which is characteristic of the deep ocean, but in the horizontal plane as well.     

Sound field variations caused by intense internal waves in a shallow sea with a weak thermocline

Results of an experiment on investigating the fluctuations of a sound signal with a frequency of 295 Hz on a stationary 32-km-long acoustic path in a shallow sea are presented. Hydrological conditions on the path were characterized by the presence of a weak thermocline and a frequent occurrence of intense internal wave trains. The space-time characteristics of these internal waves were measured in detail. Experimental evidence of the repetition of the forms of internal solitons in the variations of the amplitude and phase of an acoustic signal was obtained.     

Energy fluctuations of high-frequency sound signals in a shallow water in the presence of nonlinear internal waves

The paper presents an analysis of energy fluctuations of high-frequency (2–4.5 kHz) sound signals propagating in a shallow water in the presence of nonlinear (soliton-like) internal waves (2006 Shallow Water experiment, US Atlantic shelf). Signals were received by three single hydrophones in different directions at distances of ～4, ～12, and ～5 km from the source. The angle between the first two acoustic tracks was ～15°. The third track was almost an extension of the first and was on the other side of the source. A relatively short (one to two solitons) nonlinear internal wave packet first moved approximately along the first two tracks and then along the third track. It is demonstrated that in the presence of solitons on the track in the frequency spectrum of energy fluctuations, there is an isolated frequency that depends, in particular, on the angle between the soliton front and the acoustic track. The experimental results agree well with the theory previously proposed by the authors, where the occurrence mechanism of fluctuations is explained using the ray approach.     

Acoustic waves in random fields

The effect of space- and time-dependent random mass density, velocity, and pressure fields on frequencies and amplitudes of acoustic waves is considered by means of the analytical perturbative method. The analytical results, which are valid for weak fluctuations and long wavelength sound waves, reveal frequency and amplitude alteration, the effect of which depends on the type of random field. In particular, the effect of a random mass density field is to increase wave frequencies. Space-dependent random velocity and pressure fields reduce wave frequencies. While space-dependent random fields attenuate wave amplitudes, their time-dependent counterparts lead to wave amplification. In another example, sound waves that are trapped in the vertical direction but are free to propagate horizontally are affected by a space-dependent random mass density field. This effect depends on the direction along which the field is varying. A random field, which varies along the horizontal direction, does not couple vertically standing modes but increases their frequencies and attenuates amplitudes. These modes are coupled by a random field which depends on the vertical coordinate, but the dispersion relation remains the same as in the case of the deterministic medium.     

Nonlinear theory of transverse perturbations of quasi-one-dimensional solitons

An averaged variational principle is applied to analyze the nonlinear effect of transverse perturbations (including diffraction) on quasi-one-dimensional soliton propagation governed by various wave equations. It is shown that parameters of the spatiotemporal solitons described by the cubic Schrödinger equation and the Yajima-Oikawa model of interaction between long-and short-wavelength waves satisfy the spatial quintic nonlinear Schrödinger equation for a complex-valued function composed of the amplitude and eikonal of the soliton. Three-dimensional solutions are found for two-component “bullets” having long-and short-wavelength components. Vortex and hole-vortex structures are found for envelope solitons and for two-component solitons in the regime of resonant long/short-wave coupling. Weakly nonlinear behavior of transverse perturbations of one-dimensional soliton solutions in a self-defocusing medium is described by the Kadomtsev-Petviashvili equation. The corresponding rationally localized “lump” solutions can be considered as secondary solitons propagating along the phase fronts of the primary solitons. This conclusion holds for primary solitons described by a broad class of nonlinear wave equations.     

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).