Acoustic scattering by turbulent fluctuations of pressure and entropy

Detailed analysis is presented of the well-known Tatarskii’s formula, which describes sound wave scattering in a turbulent atmosphere. The adiabaticity of the acoustic fluctuations and incompressibility of the turbulent fluctuations are assumed only. This yields to additional 1 terms in the classical formula (probably, small in the inertial range of turbulence). We show the change of Obukhov’s formula, which describes the connection between turbulent fluctuations of pressure and velocities in a compressible atmosphere, and also demonstrate the effect of the independence of fluctuations of the potential and thermodynamic temperatures. By analogy with the formula for small-scale isotropic temperature fluctuations, which was also obtained by Obukhov, we derive a formula for the fluctuations of entropy and potential density as function of entropy, which describes spatial distribution of the probability density of identical “fluid particles” in the turbulent media.     

On a Modification of the Scintillation Method

We solve the problem of diffraction of fluctuating radiation by an optically thin irregular layer (phase screen) with developed turbulent structure. It is shown that in the case of diffraction of radiation with saturated fluctuations and a narrow-band frequency spectrum by a weakly turbulent moving phase screen, the measured frequency spectrum of intensity fluctuations in the observation plane allows one to obtain information on the form of the spectrum of irregularities of an optically thin irregular layer in a wide size range significantly exceeding the size of the first Fresnel zone. Similarly to the well-known phase method of diagnostics of randomly irregular media, the conventional scintillation method modified in such a way yields undistorted information on the form of the irregularity spectrum. However, in contrast to the phase method, it also allows one to obtain data on the drift velocity of irregularities in the studied irregular layer.     

Technique for interaction of optical fields with turbulent medium containing particles

We develop a method for transmission of stochastic fields through turbulent media (atmosphere, ocean, biotissues) containing randomly distributed particles. The method is based on the angular spectrum representation of stochastic, statistically stationary, scalar fields, the Rytov perturbation series for propagation in weakly fluctuating media, and the first Born approximation for weak scattering from particulate media. The results for transmission of the deterministic (laser) field may be obtained from our general results as a limiting case.     

On the theory of refractive radio-wave scattering

We consider in detail the frequency correlation of radio-wave fluctuations in one or several thick layers with strong large-scale inhomogeneities of turbulent origin. General expressions are obtained for the space-frequency fluctuation correlation of the radio-waves received. We analyze particular cases of radio wave scattering in turbulent media with inhomogeneities described by power-law spectra with indices p2 and p3. It is shown, in particular, that the coherence band of signals propagated in media with strong large-scale inhomogeneities is critically dependent on the spectral type of thOse inhomogeneities. The occurrence of an additional strongly scattering layer, which has radically different properties compared to the first layer, on the radio-wave path can increase or decrease considerably the frequency correlation of the radio waves received.Radiophysical Research Institute, Nizhny Novgorod. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 38, No. 10, pp. 1012–1022, October, 1995.     

Observation of laser light scattering by a turbulent gas without seeding

An experiment of laser light scattering by a turbulent highly subsonic free jet of air is presented. The originality of the method lies in the fact that no particle seeding is needed. The experimental scattering cross section, which can be interpreted from the three-dimensional spectral density of temperature fluctuations, is compared to the theoretical one obtained by turbulent mixing theories. The scattered field time correlations measured in the heterodyne mode are interpreted by considering the Doppler effect on moving turbulent eddies and compared with theory. The intensity time correlations measured in the homodyne mode are interpreted in terms of local properties of the turbulence.     

再入体缩比模型湍流等离子体电磁散射特性测量

介绍了在弹道靶上利用二级轻气炮发射再入体缩比模型开展湍流等离子体电磁散射特性模拟试验方法、湍流等离子体的雷达散射截面积(RCS)测量方法。给出了模型尾迹湍流等离子体的电磁散射特性测量典型试验结果,对获得的试验结果进行了分析,并与一阶畸变波Born方法计算结果进行了比较。结果表明:合理选择缩比模型发射速度和飞行环境压力,在弹道靶上能够模拟产生湍流等离子体;利用激光阴影成像技术获得的锥模型尾迹流场图像证实了尾迹转捩的出现及其湍流形成;在给定的试验条件下,锥模型及其绕流RCS测量值比其尾迹RCS测量值高3个数量级,比背景散射电平高0.5~2.5个数量级,且信号没有周期性,幅度脉动范围为1~15dB,频率脉动范围0.4~40kHz;锥模型湍流尾迹RCS的脉动可能是尾迹电子密度的脉动引起的;单站X波段雷达系统测量的锥模型尾迹亚密湍流等离子体的散射信号测量值与计算结果变化规律一致;弹道靶RCS测量技术可用于再入体缩比模型湍流等离子体电磁散射特性研究,为开展相关研究提供了一种有效的地面模拟实验研究途径。     

Scattering of sound waves by a turbulent wake

In this investigation, the Doppler shifted power spectrum of the scattering cross-section is obtained for plane acoustic waves scattered by fluid flow fluctuations appropriate to a turbulent wake. The wake considered in this paper is assumed almost homogeneous and isotropic and of low Reynolds number.It is shown that the evaluation of the Doppler scattering cross-section essentially reduces to the calculation of the wave number converted and frequency shifted energy spectrum function of the turbulent flow fluctuations. In prescribing the low Reynolds number turbulence spectrum, inertial forces are assumed negligible. Convective effects of the macro-eddies, which cause a Doppler shift in the scattered waves, are considered using a Lagrangian-type of space-time velocity correlation.After finding the spectrum of turbulent fluctuations, the Doppler shifted power spectrum of the scattering cross-section, which characterizes the scattered waves, is obtained explicitly for the far field approximation.     

Experimental studies of flow noise around a surfacing device

The wall pressure fluctuations in turbulent boundary layers play an important role in acoustic measurements carried out in moving media. Results of measuring the frequency spectra of wall pressure fluctuations around a surfacing device are presented. The spatial resolution achieved in measuring the wall pressure fluctuations is investigated. It is demonstrated that the results of hydrodynamic flow noise measurements strongly depend on the aperture size of the measuring acoustic transducer and its orientation in the turbulent boundary layer. The pseudosound pressure fluctuation spectra observed in a series of experiments with surfacing devices show that the resolution of the pressure receivers operating in the turbulent boundary layers considerably varies. On the basis of systematic measurements of wall pressure fluctuations by miniature and distributed receivers at high Reynolds numbers, the effect of the geometric dimensions of a pressure receiver on its resolution in the flow noise measurements is studied. An experimental method is proposed for estimating the receiver-induced distortions.     

Some effects of partial averaging of signal fluctuations in a random medium

The concept of partial averaging of signal fluctuations in a stretched turbulent medium is considered. Such uncontrollable averaging over time, frequency, or space arises from the mutual influence of signals scattered by irregularities of different scales (or different scattering layers) on fluctuations of the received signal intensity. The scintillation index of a partially averaged field is defined for the averaging action of a radiation source of finite angular dimensions. The proposed concept and obtained results may be useful in many applications as a development of the statistical theory of wave propagation in random media.Scientific-Research Institute of Radiophysics. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 37, No. 6, pp. 754–762, June, 1994.     

Collective Scattering of Electromagnetic Waves from a Relativistic Magnetized Plasma

Recently, laser and microwave scatterings have become one of the important diagnostic means for plasma. Laser and microwave correlative scattering spectrum is determined by particle-density fluctuations in a weak turbulent plasma. In a relativistic plasma, on the basis of complete electromagnetic interaction between particles, a general expression for particle density fluctuations and spectra of laser and microwave scattering from a magnetized plasma are derived. The laser and microwave scattering spectra provide information on electron density and temperature, ion temperature, resonance and nonresonance effects.     

Effect of absorption on surface speckles in random media

We investigate the intensity fluctuations of light backscattered from absorbing random media. A numerical simulation which takes into account the interference among different scattering paths reveals that the contrast of speckle patterns appearing at the surface of the medium decreases with an increase of absorption in weak absorption regime, but increases for strong absorption. It is shown from a simple theoretical model that such a contrast variation is caused by changes in the power of diffusive-scattering waves and in the amplitude distribution of single and low-order scattering waves.     

Long-range correlations in the speckle patterns of directed waves

We develop a general method for calculating statistical properties of the speckle pattern of coherent waves propagating in disordered media. In some aspects this method is similar to the Boltzmann-Langevin approach for the calculation of classical fluctuations. We apply the method to the case where the incident wave experiences many small angle scattering events during propagation, but the total angle change remains small. In many aspects our results for this case are different from results previously known in the literature. The correlation function of the wave intensity at two points separated by a distance r, has a long-range character. It decays as a power of r and changes sign. We also consider sensitivities of the speckles to changes of external parameters, such as the wave frequency and the incidence angle.     

The mean-field method in the problem of acoustic wave propagation in a turbulent atmosphere

We analyze the problem of acoustic-wave propagation in a turbulent atmosphere using the mean-field method. The equation for the sound pressure is written with accuracy up to terms that are linear with respect to the Mach number of the turbulent air flow. An expression for the attenuation constant of the mean field is obtained. For the turbulence model described by the von Kármán correlation function of fluctuations, the attenuation coefficient of the mean field is numerically studied in detail. It is shown that under typical conditions of the near-ground atmospheric layer, the predominant contribution to scattering of acoustic waves is given by the turbulent motion of the air masses. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 51, No. 5, pp. 413–424, May 2008.     

Statistics of a coherent lidar signal in a turbulent atmosphere

Absolute and conditional statistical properties of a pulse coherent Doppler lidar signal in a turbulent atmosphere are studied. Upon coherent receiving of optical fields scattered by a large number of particles, the lidar signal is shown to be a nonstationary non-Gaussian random process with Gaussian conditional statistical characteristics. The appearance of non-Gaussian properties of the signal is caused by correlation of turbulent fluctuations of the wind velocity field within the scattering volume. For the considered signal model, which corresponds to the single scattering approximation and is a sum of a large number of random variables, the central limit theorem is found to be untrue due to the statistical dependence of particles’ positions in a turbulent atmosphere. The results of numerical calculations show that, for a homogeneous and isotropic turbulence, the behavior of the signal statistics significantly depends on the size of the scattering volume and on the state of atmospheric turbulence. A Gaussian statistics is observed at small heights; with an increase in height, the non-Gaussian component becomes considerable in fluctuations of the lidar signal.     

Cross photoelastic and thermorefractive light scattering in continuous media

Two additional types of light scattering in continuous media are considered. One is the cross photoelastic scattering from density fluctuations caused by thermodynamic temperature fluctuations and the other is the cross thermorefractive scattering from temperature fluctuations caused by density fluctuations, which manifest themselves in propagation of elastic sound waves. Expressions for the light scattering coefficients for these two types of scattering are obtained. The integral intensities of scattered light are shown to be comparable with the well-known integral intensities of light scattering by fluctuations of density (pressure) and temperature (entropy) for some substances.     

New light on disordered ensembles: ab initio structure determination of one particle from scattering fluctuations of many copies

We report on the first experimental ab?initio reconstruction of an image of a single particle from fluctuations in the scattering from an ensemble of copies, randomly oriented about an axis. The method is applicable to identical particles frozen in space or time (as by snapshot diffraction from an x-ray free electron laser). These fluctuations enhance information obtainable from an experiment such as conventional small angle x-ray scattering.     

Two-dimensional measurement of density,velocity, and temperature in turbulent high-speed air flows by UV rayleigh scattering

Instantaneous cross-sectional images of turbulent air flows with densities on the order of one atmosphere or less can be obtained in a straightforward manner using far ultraviolet Rayleigh scattering. These images give quantitative values for the air density and show the details of turbulent structure, shock structure, and shock wave/boundary layer interactions. Two-dimensional spatial correlations taken from multiple images give the shape and extent of average turbulent structure as well as the coupling between turbulent structure and other flow features. This technique may be extended to observe velocity fields by either double pulsing the illumination source or by using a narrow linewidth atomic or molecular filter window in front of the detector array. The latter approach also yields temperature. Used in conjunction with flow marking techniques such as RELIEF, coupling between turbulent structure and velocity fluctuations can also be determined. These diagnostic techniques can be extended to combusting flows to observe instantaneous structure, mixing, flame front location, and velocity fields.     

Fractal structures in turbulence

We present a qualitative overview of our work on the issue of fractal structures in turbulence. We explain why fully developed turbulence is not space filling and describe how its fractal dimension can be estimated theoretically. The implications of the fractal nature of turbulence on transport processes like turbulent diffusion and on fluctuations in passive scalars are discussed. The latter affect wave propagation in turbulent media and these effects are examined. In addition we consider clouds in the atmosphere which are claimed to have fractal perimeters (or surfaces) and outline the physical reasons for this phenomenon. The fractal dimension of clouds is tied to the theory of turbulent diffusion and is computed theoretically. Indications of the road ahead are given.     

Intensity fluctuations in a moving random medium

We consider the intensity fluctuations arising when a point source of radiation moves in a randomly inhomogeneous scattering medium. The medium itself can also move with a velocity whose component normal to the direction of propagation can have an arbitrary distribution. We derive an expression for the space-time autocorrelation function of the intensity fluctuations transverse to the direction of propagation. The result is analysed for some particular cases and it is shown how the resulting information can be useful in examining the behaviour of random media in situations of practical interest.     

Estimation of co-channel interference between cities caused by ducting and turbulence

With the rapid development of the fifth-generation(5 G)mobile communication technology,the application of each frequency band has reached the extreme,causing mutual interference between different modules.Hence,there is a requirement for detecting filtering and preventing interference.In the troposphere,over-the-horizon propagation occurs in atmospheric ducts and turbulent media.The effects of both ducting and turbulence can increase the probability of occurrence of long-distance co-channel interference(CCI),in turn,severely affecting the key performance indicators such as system access,handover and drop.In the 5 G era,to ensure communication channels and information security,CCI must be reduced.This paper introduces a scattering parabolic equation algorithm for calculating signal propagation in atmospheric ducts on irregular terrain boundaries.It combines Hitney’s radio physical optical model and Wagner’s nonuniform turbulent scattering model for calculating the tropospheric scattering in an evaporation duct or a surface-based duct.The new model proposes a tropospheric scattering parabolic equation algorithm for various tropospheric duct environments.Finally,as a specific case,the topographical boundaries between several cities in the East China Plain were considered,and the over-the-horizon propagation loss was simulated for various ducting and turbulent environments.The simulation results were used to evaluate whether CCI would occur between cities in a specific environment.