Fourth moments of acoustic waves forward scattered by a rough ocean surface

Three types of statistical fourth moments of acoustic waves forward scattered by a randomly rough ocean surface are derived and numerically evaluated. The first one is related to the scintillation index which characterizes intensity fluctuations. The second one is the two-position intensity correlation function which describes the spatial correlation of wave intensity. The third is the fourth-moment two-position coherence function which carries information on the phase fluctuations of the scattered wave. In the range of weak scattering, the ratio of the absolute value of the fourth-moment two-position coherence function over the two-position intensity correlation exactly describes the mean-square fluctuation of the relative phase between the two positions. The acoustic frequency is high so that the Kirchhoff approximation can be used. Two types of spectral functions for surface-height fluctuations are considered: a Gaussian spectrum and the Donelan-Pierson spectrum. The latter is obtained from a model for the fluctuations of the ocean surface height which are controlled by the wind speed at the ocean surface.     

Fourth moments of acoustic waves forward scattered by a rough ocean surface

Abstract

Three types of statistical fourth moments of acoustic waves forward scattered by a randomly rough ocean surface are derived and numerically evaluated. The first one is related to the scintillation index which characterizes intensity fluctuations. The second one is the two-position intensity correlation function which describes the spatial correlation of wave intensity. The third is the fourth-moment two-position coherence function which carries information on the phase fluctuations of the scattered wave. In the range of weak scattering, the ratio of the absolute value of the fourth-moment two-position coherence function over the two-position intensity correlation exactly describes the mean-square fluctuation of the relative phase between the two positions. The acoustic frequency is high so that the Kirchhoff approximation can be used. Two types of spectral functions for surface-height fluctuations are considered: a Gaussian spectrum and the Donelan-Pierson spectrum. The latter is obtained from a model for the fluctuations of the ocean surface height which are controlled by the wind speed at the ocean surface.     

Transverse-longitudinal coherence function of a sound field for line-of-sight propagation in a turbulent atmosphere

Using the narrow-angle and Markov approximations, a formula for the transverse-longitudinal coherence function of a sound field propagating in a turbulent atmosphere with temperature and wind velocity fluctuations is derived. This function, which applies to observation points that are arbitrarily located in space, generalizes the transverse coherence function (coherence when the observation points are in a plane perpendicular to the sound propagation path), which has been studied extensively. The new result is expressed in terms of the transverse coherence function and the extinction coefficient of the mean sound field. The transverse-longitudinal coherence function of a plane sound wave is then calculated and studied in detail for the Gaussian and von Kármán spectra of temperature and wind velocity fluctuations. It is shown, for relatively small propagation distances, that the magnitude of the coherence function decreases in the longitudinal direction but remains almost constant in the transverse direction. On the other hand, for moderate and large propagation distances, the magnitude of the coherence decreases faster in the transverse direction than in the longitudinal. For some parameters of the problem, the coherence function has relatively large local maxima and minima as the transverse and longitudinal coordinates are varied. With small modifications, many results obtained in the paper can be applied to studies of electromagnetic wave propagation in a turbulent atmosphere.     

Monostatic lidar in weak-to-strong turbulence

Abstract

A heuristic scintillation model previously developed for weak-to-strong irradiance fluctuations of a spherical wave is extended in this paper to the case of a monostatic lidar configuration. As in the previous model, we account for the loss of spatial coherence as the optical wave propagates through atmospheric turbulence by eliminating the effects of certain turbulent scale sizes that exist between the scale size of the spatial coherence radius of the beam and that of the scattering disc. These mid-range scale-size effects are eliminated through the formal introduction of spatial scale frequency filters that continually adjust spatial cut-off frequencies as the optical wave propagates. In addition, we also account for correlations that exist in the incident wave to the target and the echo wave from the target arising from double-pass propagation through the same random inhomogeneities of the atmosphere. We separately consider the case of a point target and a diffuse target, concentrating on both the enhanced backscatter effect in the mean irradiance and the increase in scintillation in a monostatic channel. Under weak and strong irradiance fluctuations our asymptotic expressions are in agreement with previously published asymptotic results.     

Effects of a modified spectral model on the spatial coherence of a laser beam

The influence of a modified (bump) spectrum of refractive index fluctuations on the spatial coherence of an optical wave is studied here and compared with that based on a von Karman spectrum. Analytical expressions are derived for the mutual coherence function (MCF) and wave structure function (WSF) of a lowest-order Gaussian beam wave from which the beam spot size and degree of coherence are deduced. The qualitative behaviour of beam spreading and coherence length is basically the same for both spectral models. Also, when the radius of the Fresnel zone and initial beam radius are of comparable size, the presence of a spectral bump appears to have minimal effect on spatial coherence for all beams. However, the choice of spectral model is important for certain ranges of parameters. In particular, the implied spatial coherence length for a collimated beam based on the modified spectrum is significantly smaller than that based on the von Karman spectrum whenever the Fresnel zone is either much larger or much smaller than the initial beam radius, whereas for a focused beam the predicted coherence length based on the modified spectrum is slightly larger when the Fresnel zone size is much smaller than the initial beam radius.     

海洋湍流中光波特征参量和短期光束扩展的研究

Nikishov等建立的海洋湍流功率谱模型中,假设了海水有着稳定的分层.但是,实际海水通常不是稳定分层的,温度与盐度的涡流扩散率是不相等的.2017年,Elamassie等建立了考虑这些因素的更合理的海洋湍流功率谱模型.湍流介质中光波空间相干长度等基本特征参量在表征湍流强度和光传输相位校正技术等方面起着重要作用.本文基于Elamassie海洋湍流功率谱模型,重新推导出了海洋湍流中光波结构函数、光波空间相干长度和Fried参数的解析公式,并校验了所得公式的正确性.研究发现：当温度变化引起的光学湍流占主导地位时,Nikishov海洋湍流功率谱模型把湍流强度低估了;当盐度变化引起的光学湍流占主导地位时,Nikishov海洋湍流功率谱模型把湍流强度高估了.基于Elamassie海洋湍流功率谱模型,本文推导出了高斯光束短期光束扩展的半解析公式,并验证了其正确性.研究还表明：海水稳定分层与否,短期光束扩展差异很大.本文研究结果对水下湍流环境中的光通信、成像和传感等应用具有重要意义.     

Sound-wave coherence in atmospheric turbulence with intrinsic and global intermittency

The coherence function of sound waves propagating through an intermittently turbulent atmosphere is calculated theoretically. Intermittency mechanisms due to both the turbulent energy cascade (intrinsic intermittency) and spatially uneven production (global intermittency) are modeled using ensembles of quasiwavelets (QWs), which are analogous to turbulent eddies. The intrinsic intermittency is associated with decreasing spatial density (packing fraction) of the QWs with decreasing size. Global intermittency is introduced by allowing the local strength of the turbulence, as manifested by the amplitudes of the QWs, to vary in space according to superimposed Markov processes. The resulting turbulence spectrum is then used to evaluate the coherence function of a plane sound wave undergoing line-of-sight propagation. Predictions are made by a general simulation method and by an analytical derivation valid in the limit of Gaussian fluctuations in signal phase. It is shown that the average coherence function increases as a result of both intrinsic and global intermittency. When global intermittency is very strong, signal phase fluctuations become highly non-Gaussian and the average coherence is dominated by episodes with weak turbulence.     

Pulse broadening and two-frequency mutual coherence function of the scattered wave from rough surfaces

Analytical expressions for the two-frequency mutual coherence function and angular correlation function of the scattered wave from rough surfaces based on the Kirchhoff approximation are presented. The coherence bandwidth depends on the illumination area as well as on the incident and scattered angles and the surface characteristics. Scattered pulse shapes are calculated as the Fourier transform of the two-frequency mutual coherence function. Calculations based on analytical solutions are compared with millimetre wave experimental data and Monte Carlo simulations showing good agreement.     

Auto- versus Cross-Correlation Noise in Periodically Driven Quantum Coherent Conductors

Expressing currents and their fluctuations at the terminals of a multi-probe conductor in terms of the wave functions of carriers injected into the Fermi sea provides new insight into the physics of electric currents. This approach helps us to identify two physically different contributions to shot noise. In the quantum coherent regime, when current is carried by non-overlapping wave packets, the product of current fluctuations in different leads, the cross-correlation noise, is determined solely by the duration of the wave packet. In contrast, the square of the current fluctuations in one lead, the autocorrelation noise, is additionally determined by the coherence of the wave packet, which is associated with the spread of the wave packet in energy. The two contributions can be addressed separately in the weak back-scattering regime, when the autocorrelation noise depends only on the coherence. Analysis of shot noise in terms of these contributions allows us, in particular, to predict that no individual traveling particles with a real wave function, such as Majorana fermions, can be created in the Fermi sea in a clean manner, that is, without accompanying electron–hole pairs.     

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.     

Pulse broadening and two-frequency mutual coherence function of the scattered wave from rough surfaces

Abstract

Analytical expressions for the two-frequency mutual coherence function and angular correlation function of the scattered wave from rough surfaces based on the Kirchhoff approximation are presented. The coherence bandwidth depends on the illumination area as well as on the incident and scattered angles and the surface characteristics. Scattered pulse shapes are calculated as the Fourier transform of the two-frequency mutual coherence function. Calculations based on analytical solutions are compared with millimetre wave experimental data and Monte Carlo simulations showing good agreement.     

湍流大气传输高斯谢尔光束的到达角起伏

研究了在弱大气湍流起伏环境下以窄带宽高斯谢尔光束为激光光源的大气通信问题,分析了大气湍流强度和光源空间相干度对通信光束到达角起伏的影响.采用窄带宽光场的交叉谱密度函数代替光场互相干函数的近似方法和采用包含大气湍流内外尺度的简化折射率谱密度函数,得出了湍流大气中传输高斯谢尔光束的波结构函数(WSF) 和到达角起伏方差解析近似关系.分析表明,光源的空间相干度和传输光束的湍流扩展是影响高斯谢尔光束的相位起伏结构函数和传输光束到达角起伏的重要因素.     

Theory of optical scintillation: Gaussian-beam wave model

Abstract

A scintillation model previously developed by the authors is extended in this paper to the case of a propagating Gaussian-beam wave. As in the previous model, we account for the loss of spatial coherence as the optical wave propagates through atmospheric turbulence by eliminating effects of certain turbulent scale sizes that exist between the scale size of the spatial coherence radius of the beam and that of the scattering disc. These mid-range scale-size effects are eliminated through the formal introduction of spatial frequency filters that continually adjust spatial cut-off frequencies as the optical wave propagates. Unlike the previous model, in this paper we include the effect of a finite outer scale in addition to the inner scale. With a finite outer scale, the scintillation index can be substantially lower in strong turbulence than that predicted by a model with an infinite outer scale. This particular behaviour of scintillation in strong turbulence, mostly associated with horizontal paths near the ground, cannot be explained on the basis of previous expressions deduced from the asymptotic theory. Comparisons of the scintillation models with published experimental and simulation data through weak and strong irradiance fluctuations show excellent fits.     

Coherence and interference in diffuse noise: on the information and statistics associated with spatial wave correlations in directional noise fields

Broadband noise correlation methods for the passive extraction of information about the propagation of waves between distant sensor locations have received considerable attention in the literature. For the case of an isotropic ambient field distribution, there is a well-defined relationship between the expectation value of the wave coherence over the sensors and point-to-point wave propagation. Experimental applications, however, must contend with ambient field anisotropy as well as the performance limitations associated with stochastic fluctuations. This paper explores the influence of ambient field directionality on both (1) the connection between the measured wave coherence and sensor-to-sensor propagation and on (2) the rate at which measurements stochastically converge to the expectation value of the underlying wave coherence. Due to diffraction, the relationship between the measured wave coherence and sensor-to-sensor propagation is shown to be robust to even highly directional ambient field features. While the fluctuations of a stochastic system are generally known to depend on bandwidth and measurement duration, the rate of stochastic convergence depends additionally on the cross-spectral power density (coherent power) relative to the power-spectral density (total incident power). Practical experimental implications of these results are discussed.     

Monitoring of the ducting by a ground-based GPS receiver

In this paper, we describe the estimation of low-altitude refractivity structure from simulation and real ground-based GPS delays. The vertical structure of the refractive environment is modeled using three parameters, i.e., duct height, duct thickness, and duct slope. The refractivity model is implemented with a priori constraints on the duct height, thickness, and strength, which might be derived from soundings or numerical weather-prediction models. A ray propagation model maps the refractivity structure into a replica field. Replica fields are compared with the simulation observed data using a squared-error objective function. A global search for the three environmental parameters is performed using genetic algorithm. The inversion is assessed by comparing the refractivity profiles from the radiosondes to those estimated. This technique could provide near-real-time estimation of ducting effect. The results suggest that ground-based GPS provides significant atmospheric refractivity information, despite certain fundamental limitations of ground-based measurements. Radiosondes typically are launched just a few times daily. Consequently, estimates of temporally and spatially varying refractivity that assimilate GPS delays could substantially improve over-estimates using radiosonde data alone.     

一种简化非Gauss场模型在随机介质中光传播问题中的应用

为了研究大气湍流间歇性的光传播效应，构造出一种比较简单的非Gauss场模型(Poission场 )用于描述大气介电常数(或折射率)随机起伏.模型特征泛函含有四个待定函数，根据大气湍 流的统计均匀性，介电起伏的单点概率分布函数，以及介电起伏能谱可以选择或确定它们. 对在这种简化湍流中传播的光波平均场及二阶统计矩性质进行了理论分析，并给出数值模拟 的一个简单例子. 关键词： 光波传播 大气湍流 间歇性     

Inversion for atmosphere duct parameters using real radar sea clutter

This paper addresses the problem of estimating the lower atmospheric refractivity (M profile) under nonstandard propagation conditions frequently encountered in low altitude maritime radar applications. The vertical structure of the refractive environment is modeled using five parameters and the horizontal structure is modeled using five parameters. The refractivity model is implemented with and without a priori constraint on the duct strength as might be derived from soundings or numerical weather-prediction models. An electromagnetic propagation model maps the refractivity structure into a replica field. Replica fields are compared with the observed clutter using a squared-error objective function. A global search for the 10 environmental parameters is performed using genetic algorithms. The inversion algorithm is implemented on the basis of S-band radar sea-clutter data from Wallops Island, Virginia (SPANDAR). Reference data are from range-dependent refractivity profiles obtained with a helicopter. The inversion is assessed (ⅰ) by comparing the propagation predicted from the radar-inferred refractivity profiles with that from the helicopter profiles, (ⅱ) by comparing the refractivity parameters from the helicopter soundings with those estimated. This technique could provide near-real-time estimation of ducting effects.     

Monitoring of ducting by using a ground-based GPS receiver

In this paper,we describe the estimation of low-altitude refractivity structure from simulation and real ground-based GPS delays.The vertical structure of the refractive environment is modeled using three parameters,i.e.,duct height,duct thickness,and duct slope.The refractivity model is implemented with a priori constraints on the duct height,thickness,and strength,which might be derived from soundings or numerical weather-prediction models.A ray propagation model maps the refractivity structure into a replica field.Replica fields are compared with the simulation observed data using a squarederror objective function.A global search for the three environmental parameters is performed using a genetic algorithm.The inversion is assessed by comparing the refractivity profiles from the radiosondes to those estimated.This technique could provide near-real-time estimation of the ducting effect.The results suggest that ground-based GPS provides significant atmospheric refractivity information,despite certain fundamental limitations of ground-based measurements.Radiosondes are typically launched just a few times daily.Consequently,estimates of temporally and spatially varying refractivity that assimilate GPS delays could substantially improve over-estimates caused by using radiosonde data alone.     

Wave motion of incompressible turbulent fluid

Evolution of small disturbances in a fully developed incompressible turbulent flow is considered on the base of the transport equation for the single-point probability density function (PDF) of velocity fluctuations. It is shown that at high frequencies this equation is similar to the Vlasov equation for charged plasma in a self-consistent electromagnetic field having longitudinal wave solutions for turbulent stresses similar to Langmuir waves. It is found that the longitudinal waves of turbulent stresses have a constant phase velocity and can be damped, neutral, or growing waves, depending on the type of undisturbed probability density function of velocity fluctuations. The obtained result differs from the previously published solutions to this problem using the statistical moments closures according to which the wave disturbances should be neutral or damped. The possibilities of experimental observation of longitudinal waves of turbulent stresses are analyzed.     

The estimation of lower refractivity uncertainty from radar sea clutter using the Bayesian-MCMC method

The estimation of lower atmospheric refractivity from radar sea clutter(RFC) is a complicated nonlinear optimization problem.This paper deals with the RFC problem in a Bayesian framework.It uses the unbiased Markov Chain Monte Carlo(MCMC) sampling technique,which can provide accurate posterior probability distributions of the estimated refractivity parameters by using an electromagnetic split-step fast Fourier transform terrain parabolic equation propagation model within a Bayesian inversion framework.In contrast to the global optimization algorithm,the Bayesian-MCMC can obtain not only the approximate solutions,but also the probability distributions of the solutions,that is,uncertainty analyses of solutions.The Bayesian-MCMC algorithm is implemented on the simulation radar sea-clutter data and the real radar seaclutter data.Reference data are assumed to be simulation data and refractivity profiles are obtained using a helicopter.The inversion algorithm is assessed(i) by comparing the estimated refractivity profiles from the assumed simulation and the helicopter sounding data;(ii) the one-dimensional(1D) and two-dimensional(2D) posterior probability distribution of solutions.