Calculations of internal-wave-induced fluctuations in ocean-acoustic propagation

Variability in the ocean sound-speed field on time scales of a few hours and horizontal spatial scales of a few kilometers is often dominated by the random, anisotropic fluctuations caused by the internal-wave field. Results have been compiled from analytical approaches and from numerical simulations using the parabolic approximation into an efficient set of algorithms for calculating approximations to internal-wave effects on temporal and spatial coherences, coherent bandwidths, and regimes of acoustic fluctuation behavior. These approximate formulas account for the background, deterministic, sound-speed profile and the anisotropy of the internal-wave field, and they also allow for the incorporation of experimentally determined profiles of sound speed, buoyancy frequency, and sound-speed variance. The algorithms start from the geometrical-acoustics approximation, in which the field transmitted from a source can be described completely in terms of rays whose characteristics are determined by the sound speed as a function of position. Ordinary integrals along these rays provide approximations to acoustic-fluctuation quantities due to the statistical effects of internal waves, including diffraction. The results from the algorithms are compared with numerical simulations and with experimental results for long-range propagation in the deep ocean.     

Comparison between ocean-acoustic fluctuations in parabolic-equation simulations and estimates from integral approximations

Line-integral approximations to the acoustic path integral have been used to estimate the magnitude of the fluctuations in an acoustic signal traveling through an ocean filled with internal waves. These approximations for the root-mean-square (rms) fluctuation and the bias of travel time, rms fluctuation in a vertical arrival angle, and the spreading of the acoustic pulse are compared here to estimates from simulations that use the parabolic equation (PE). PE propagations at 250 Hz with a maximum range of 1000 km were performed. The model environment consisted of one of two sound-speed profiles perturbed by internal waves conforming to the Garrett-Munk (GM) spectral model with strengths of 0.5, 1, and 2 times the GM reference energy level. Integral-approximation (IA) estimates of rms travel-time fluctuations were within statistical uncertainty at 1000 km for the SLICE89 profile, and in disagreement by between 20% and 60% for the Canonical profile. Bias estimates were accurate for the first few hundred kilometers of propagation, but became a strong function of time front ID beyond, with some agreeing with the PE results and others very much larger. The IA structure functions of travel time with depth are predicted to be quadratic with the form theta(2)vc0(-2)deltaz(2), where deltaz is vertical separation, c0 is a reference sound speed, and thetav is the rms fluctuation in an arrival angle. At 1000 km, the PE results were close to quadratic at small deltaz, with values of thetav in disagreement with those of the integral approximation by factors of order 2. Pulse spreads in the PE results were much smaller than predicted by the IA estimates. Results imply that acoustic tomography of internal waves at ranges up to 1000 km can use the IA estimate of travel-time variance with reasonable reliability.     

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.     

An Investigation of the Effects of Internal Waves on Sound Propagation in a Stratified Medium with a Sloping Bed

Internal waves usually cause temporal and spatial changes of density and consequently affect the acoustic wave propagation in the ocean. The purpose of this study is a laboratory investigation of the effects of internal waves generated by oscillation of a cylinder in a large stratified glass tank with a sloping bed on the sound waves propagation. Results showed that sound waves are affected by internal waves that depend on the slope angle to the direction of internal wave propagation angle ratio. When the ratio is subcritical or supercritical, the acoustic signal is much reduced as compared to the case with no sloped bottom. This can be explained in terms of the internal waves energy reaching the sloped bed and their reflections.     

采用小生境遗传算法反演浅海声速剖面研究*

针对浅海声速剖面反演问题,采用小生境遗传算法,结合声线搜索的最快本征声线匹配反演,实现浅海负跃层条件下的声速剖面估计。利用经验正交函数对声速剖面的多参数不确定性降维,依据声场计算模型获取的最快特征声线传播时延与观测声传播时长进行匹配,采用小生境遗传优化算法,获取最优经验正交函数估计,实现声速剖面反演。按上述方法反演处理浅海声传播实验数据,结果表明,该方法针能够有效反演浅海声速剖面,并且显著优于传统遗传算法反演结果。     

Ray chaos and ray clustering in an ocean waveguide

We consider ray propagation in a waveguide with a designed sound-speed profile perturbed by a range-dependent perturbation caused by internal waves in deep ocean environments. The Hamiltonian formalism in terms of the action and angle variables is applied to study nonlinear ray dynamics with two sound-channel models and three perturbation models: a single-mode perturbation, a randomlike sound-speed fluctuations, and a mixed perturbation. In the integrable limit without any perturbation, we derive analytical expressions for ray arrival times and timefronts at a given range, the main measurable characteristics in field experiments in the ocean. In the presence of a single-mode perturbation, ray chaos is shown to arise as a result of overlapping nonlinear ray-medium resonances. Poincare maps, plots of variations of the action per ray cycle length, and plots with rays escaping the channel reveal inhomogeneous structure of the underlying phase space with remarkable zones of stability where stable coherent ray clusters may be formed. We demonstrate the possibility of determining the wavelength of the perturbation mode from the arrival time distribution under conditions of ray chaos. It is surprising that coherent ray clusters, consisting of fans of rays which propagate over long ranges with close dynamical characteristics, can survive under a randomlike multiplicative perturbation modelling sound-speed fluctuations caused by a wide spectrum of internal waves.     

Observations of sound-speed fluctuations on the New Jersey continental shelf in the summer of 2006

Environmental sensors moored on the New Jersey continental shelf tracked constant density surfaces (isopycnals) for 35 days in the summer of 2006. Sound-speed fluctuations from internal-wave vertical isopycnal displacements and from temperature/salinity variability along isopycnals (spiciness) are analyzed using frequency spectra and vertical covariance functions. Three varieties of internal waves are studied: Diffuse broadband internal waves (akin to waves fitting the deep water Garrett/Munk spectrum), internal tides, and, to a lesser extent, nonlinear internal waves. These internal-wave contributions are approximately distinct in the frequency domain. It is found that in the main thermocline spicy thermohaline structure dominates the root mean square sound-speed variability, with smaller contributions coming from (in order) nonlinear internal waves, diffuse internal waves, and internal tides. The frequency spectra of internal-wave displacements and of spiciness have similar form, likely due to the advection of variable-spiciness water masses by horizontal internal-wave currents, although there are technical limitations to the observations at high frequency. In the low-frequency, internal-wave band the internal-wave spectrum follows frequency to the -1.81 power, whereas the spice spectrum shows a -1.73 power. Mode spectra estimated via covariance methods show that the diffuse internal-wave spectrum has a smaller mode bandwidth than Garrett/Munk and that the internal tide has significant energy in modes one through three.     

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.     

Using streamlines to visualize acoustic energy flow across boundaries

For spherical waves that radiate from a point source in a homogeneous fluid and propagate across a plane boundary into a dissimilar homogeneous fluid, the acoustic field may differ significantly from the geometric acoustic approximation if either the source or receiver is near the interface (in acoustic wavelengths) or if the stationary phase path is near the critical angle. In such cases, the entire acoustic field must be considered, including inhomogeneous waves associated with diffraction (i.e., those components that vanish with increasing frequency). The energy flow from a continuous-wave monopole point source across the boundary is visualized by tracing acoustic streamlines: those curves whose tangent at every point is parallel to the local acoustic intensity vector, averaged over a wave cycle. It is seen that the acoustic energy flow is not always in line with the "Snell's law" or stationary phase path. Also, plots of acoustic energy streamlines do not display unusual behavior in the vicinity of the critical angle. Finally, it is shown that there exists a law of refraction of acoustic energy streamlines at boundaries with density discontinuities analogous to Snell's law of refraction of ray paths across sound speed discontinuities. Examples include water-to-seabed transmission and water-to-air transmission.     

Statistics of low-frequency normal-mode amplitudes in an ocean with random sound-speed perturbations: shallow-water environments

Second- and fourth-moment mode-amplitude statistics for low-frequency ocean sound propagation through random sound-speed perturbations in a shallow-water environment are investigated using Monte Carlo simulations and a transport theory for the cross-mode coherence matrix. The acoustic observables of mean and mean square intensity are presented and the importance of adiabatic effects and cross-mode coherence decay are emphasized. Using frequencies of 200 and 400 Hz, transport theory is compared with Monte Carlo simulations in a canonical shallow-water environment representative of the summer Mid-Atlantic Bight. Except for ranges less than a horizontal coherence length of the sound structure, the intensity moments from the two calculations are in good agreement. Corrections for the short range behavior are presented. For these frequencies the computed mode coupling rates are extremely small, and the propagation is strongly adiabatic with a rapid decay of cross-mode coherence. Coupling effects are predicted to be important at kilohertz frequencies. Decay of cross-mode coherence has important implications for acoustic interactions with nonlinear internal waves: For the case in which the acoustic path is not at glancing incidence with a nonlinear internal-wave front, adiabatic phase randomizing effects lead to a significantly reduced influence of the nonlinear waves on both mean and mean square intensity.     

Ray stability in weakly range-dependent sound channels

Ray stability is investigated in environments consisting of a range-independent background sound-speed profile on which a range-dependent perturbation is superimposed. Theoretical arguments suggest and numerical results confirm that ray stability is strongly influenced by the background sound speed profile. Ray instability is shown to increase with increasing magnitude of alpha(I)=(I/omega)d omega/dI, where 2pi/omega(I) is the range of a ray double loop and I is the ray action variable. This behavior is illustrated using internal-wave-induced scattering in deep ocean environments and rough surface scattering in upward refracting environments.     

Rogue internal waves in the ocean: Long wave model

Rogue waves can be categorized as unexpectedly large waves, which are temporally and spatially localized. They have recently received much attention in the water wave context, and also been found in nonlinear optical fibers. In this paper, we examine the issue of whether rogue internal waves can be found in the ocean. Because large-amplitude internal waves are commonly observed in the coastal ocean, and are often modeled by weakly nonlinear long wave equations of the Korteweg-de Vries type, we focus our attention on this shallow-water context. Specifically, we examine the occurrence of rogue waves in the Gardner equation, which is an extended version of the Korteweg-de Vries equation with quadratic and cubic nonlinearity, and is commonly used for the modelling of internal solitary waves in the ocean. Importantly, we choose that version of the Gardner equation for which the coefficient of the cubic nonlinear term and the coefficient of the linear dispersive term have the same sign, as this allows for modulational instability. From numerical simulations of the evolution of a modulated narrow-band initial wave field, we identify several scenarios where rogue waves occur.     

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.     

南海东沙海域线性内波引起的声场统计特性

海洋内波对声传播及水声探测具有重要影响.利用南海东沙附近海域一次低频声传播起伏实验同步获取的声学与水文观测数据,从水文连续观测数据中提取了内波特征参数,验证了修正线性内波频谱公式,用蒙特卡洛方法统计分析了存在线性内波条件下的声场起伏特性,并用射线理论解释了声源与跃层相对位置对声场起伏的影响机理.结果 表明:随着频率、平...     

Formation of Brillouin waves in the underwater sound channel

The mechanism of the vertical sound field structure formation in the underwater sound channel is considered. The calculations are performed by the ray method for the rays that have upper turning points at the ocean surface. It is shown that the vertical field structure is formed by the ray pairs producing opposing waves in the vertical. The rays belonging to one pair have the same sign of their departure angles at the source. The pairs are formed because of the presence of a minimum in the ray cycle length as a function of the departure angle. The resulting ray pairs are analogs of Brillouin waves.     

Predicting acoustic effects of internal waves from the basic climatology of the world ocean

Internal waves of a given strength will produce acoustic effects that vary from water mass to water mass. Presented here is a means of predicting the strength of acoustic fluctuations due to internal waves, given the basic climatology, that is, measurements of depth, temperature, and salinity of an oceanic region. An acoustic fluctuation strength parameter F is defined as the ratio of the fractional potential sound-speed change to the fractional potential-density change. Here F is calculated at three depth levels (275, 550, and 850 m), on a one-degree grid of latitude and longitude, using NODC/OCL's World Ocean Atlas 1994. Representative values of F are presented for 15 upper water masses that range from F = 5 in the North Pacific to F = 34 in the North Atlantic, with a typical value for most of the upper waters being F = 15. Results for two depth levels within 12 intermediate water masses range from F = 7 in the North Pacific to F = 62 in the North Atlantic, with a typical value of F = 20, although there is considerable variation. In general, F exhibits higher values in the Atlantic Basin than in the Indian or Pacific, and has a maximum at 550 m. The main use of F will be the prediction of travel-time fluctuations in acoustic propagation experiments, which will be proportional to the value of F, given a universal strength of internal waves.     

The impact of water column variability on horizontal wave number estimation and mode based geoacoustic inversion results

The influence of water column variability on low-frequency, shallow water geoacoustic inversion results is considered. The data are estimates of modal eigenvalues obtained from measurements of a point source acoustic field using a horizontal aperture array in the water column. The inversion algorithm is based on perturbations to a background waveguide model with seabed properties consistent with the measured eigenvalues. Water column properties in the background model are assumed to be known, as would be obtained from conductivity, temperature, and depth measurements. The scope of this work in addressing the impact of water column variability on inversion is twofold. Range-dependent propagation effects as they pertain to eigenvalue estimation are first considered. It is shown that mode coupling is important even for weak internal waves and can enhance modal eigenvalue estimates. Second, the effect of the choice of background sound speed profile in the water column is considered for its impact on the estimated bottom acoustic properties. It is shown that a range-averaged sound velocity profile yields the best geoacoustic parameter estimates.