Vladimir E. Ostashev

Spectral broadening of sound scattered by advecting atmospheric turbulence

Scattering and spectral broadening of a monochromatic sound wave by atmospheric turbulence that is flowing with a uniform constant horizontal wind is considered. The acoustic source and a detector are at rest and at different positions in a ground-fixed frame. Analytic expressions are derived for the sound pressure scattered to the detector by a single eddy. Since distances and the scattering angle change with time as the eddy flows through the scattering volume, the detector signal has time-dependent amplitude and frequency, for which general formulas are derived. A computer code is developed that calculates the scattered signal and its Fourier transform from a single eddy, or from a steady-state collection of eddies of many different scale lengths that represents isotropic homogeneous turbulence flowing with the wind. The code utilizes a time-shift algorithm that reduces the calculation time substantially. Several numerical results from this code are presented, including simulations of a recent experiment. The predicted spectral shape, including peak width and jaggedness, are in good agreement with experiment.

Recent progress in acoustic tomography of the atmosphere

Acoustic tomography of the atmospheric surface layer is based on measurements of travel times of sound propagation among different pairs of sources and receivers usually located several meters above the ground on a horizontal scale of about 100 m. The measured travel times are used as input data in an inverse algorithm for reconstruction of temperature and wind velocity fields. Improved knowledge of these fields is important in boundary layer meteorology, theories of turbulence, and studies of electromagnetic and acoustic wave propagation in the atmosphere. In this paper, a short overview and current status of acoustic travel-time tomography of the atmosphere are presented. A brief description of a 3D array for acoustic tomography of the atmosphere which is being built at the Boulder Atmospheric Observatory is given. Furthermore, different inverse algorithms for reconstruction of temperature and velocity fields are discussed, including stochastic inversion and a recently developed time-dependent stochastic inversion. The latter inverse algorithm was used to reconstruct temperature and wind velocity fields in acoustic tomography experiments. Examples of the reconstructed fields are presented and discussed.

Time-dependent stochastic inversion in acoustic tomography of the atmosphere with reciprocal sound transmission

Time-dependent stochastic inversion (TDSI) was recently developed for acoustic travel-time tomography of the atmosphere. This type of tomography allows reconstruction of temperature and wind-velocity fields given the location of sound sources and receivers and the travel times between all source–receiver pairs. The quality of reconstruction provided by TDSI depends on the geometry of the transducer array. However, TDSI has not been studied for the geometry with reciprocal sound transmission. This paper is focused on three aspects of TDSI. First, the use of TDSI in reciprocal sound transmission arrays is studied in numerical and physical experiments. Second, efficiency of time-dependent and ordinary stochastic inversion (SI) algorithms is studied in numerical experiments. Third, a new model of noise in the input data for TDSI is developed that accounts for systematic errors in transducer positions. It is shown that (i) a separation of the travel times into temperature and wind-velocity components in tomography with reciprocal transmission does not improve the reconstruction, (ii) TDSI yields a better reconstruction than SI and (iii) the developed model of noise yields an accurate reconstruction of turbulent fields and estimation of errors in the reconstruction.

Moment-screen method for wave propagation in a refractive medium with random scattering

Direct numerical solution of a parabolic equation (PE) for the second moment of the sound field in a refracting medium with random scattering is described. The method determines the mean-square sound pressure without requiring generation of random realizations of the propagation medium. The second-moment matrix is factored into components that are independently propagated with a conventional PE algorithm. A moment screen is periodically applied to attenuate the coherence of the wavefield, much as phase screens are often applied in the method of random realizations. An example involving upwind and downwind propagation in the near-ground atmosphere shows that the new direct method converges to an accurate solution faster than the method of random realizations and is particularly well suited to calculations at low frequencies.

Development of a high-fidelity simulation capability for battlefield acoustics.

Findings are presented from the first year of a joint project between the U.S. Army Engineer Research and Development Center, the U.S. Army Research Laboratory, and the Sandia National Laboratories. The purpose of the project is to develop a finite-difference, time-domain (FDTD) capability for simulating the acoustic signals received by battlefield acoustic sensors. Many important effects, such as scattering from trees and buildings, interactions with dynamic atmospheric wind and temperature fields, and nonstationary target properties, can be accommodated by the simulation. Such a capability has much potential for mitigating the need for costly field data collection and furthering the development of robust identification and tracking algorithms. The FDTD code is based on a carefully derived set of first-order differential equations that is more general and accurate than most current sound propagation formulations. For application to three-dimensional problems of practical interest in battlefield acoustics, the code must be run on massively parallel computers. Some example computations involving sound propagation in a moving atmosphere and propagation in the presence of trees and barriers are presented.

Coherence function of a spherical acoustic wave after passing through a turbulent jet

Abstract The paper deals with a comparison between experimental data obtained by Blanc-Benon (1984) and theoretical predictions of the coherence function of a spherical sound wave after passing through a turbulent jet. The predictions are based on the theory of sound propagation in moving random media recently developed by Ostashev (1994 , 1997), which correctly takes into account the effects of an isotropic vector random field of the medium velocity fluctuations on line-of-sight sound propagation. It is shown that the theoretical predictions fit the data well.

Quasi-wavelet formulations of turbulence and wave scattering

Quasi-wavelets (QWs) are particle-like entities similar to customary wavelets in that they are based on translations and dilations of a spatially localized parent function. The positions and orientations are, however, normally taken to be random. Random fields such as turbulence may be usefully represented as ensembles of QWs with appropriately selected size distributions, number densities, and amplitudes. This paper provides an overview of previous results concerning QWs. The points of emphasis are the following. (1) Self-similar ensembles of QWs with rotation rates scaling according to Kolmogorovs hypotheses naturally produce classical inertial-subrange and von Karman-like spectra. (2) The spatially localized nature of QWs can be advantageous in wave-scattering calculations and other applications. The scattered wavefield from a single QW can be readily derived and then integrated over scale and volume to obtain expressions for the total scattering cross section. (3) Anistropy, and momentum and heat transfer, in surface-layer turbulence can be described by introducing preferred orientations and correlations among QWs representing temperature and velocity perturbations. (4) Unlike Fourier modes, QWs can be naturally arranged in a spatially intermittent manner. Models for both local (intrinsic) and global intermittency are described.

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.

Sound scattering cross-section in a stratified moving atmosphere

For a realistic model of a stratified moving atmosphere with arbitrary vertical profiles of the adiabatic sound speed and wind velocity vector, an equation is derived for the sound scattering cross-section per unit volume, σ, as a function of apparent scattering angle Θ0. The effects of these profiles on σ are studied numerically. It is shown that if the wind velocity is zero, but the adiabatic sound speed varies with height, then σ can be affected significantly for Θ0<110°. Furthermore, if the wind velocity varies with height, but the adiabatic sound speed does not, then σ can be affected significantly for Θ0<110° as well as Θ0 near 180°. These and other numerical calculations have shown that in many cases acoustic remote sensing of the structure parameters of temperature and wind velocity fluctuations in the atmosphere should be based on the derived equation for σ rather than on that used in the literature. The derived equation for σ is also compared to those obtained by Clifford and Brown [J. Acoust. S...

Wide‐angle parabolic equation in moving inhomogeneous media

The wide‐angle parabolic equation has been used widely to predict a sound field in an ocean with variations in the adiabatic sound speed c. The same equations with c replaced by the effective sound speed ceff=c+vx has recently been adopted for calculations of sound propagation in a stratified and/or turbulent atmosphere. Here, vx is the wind velocity component in the direction from a source to a receiver. However, as is shown in the presentation, such a replacement does not allow one to correctly take into account the effects of the medium velocity v on sound propagation and scattering in a wide‐angle approximation. Furthermore, the effects of fluctuations in the density ρ on sound scattering are also omitted in this approach. In the presentation, a correct wide‐angle parabolic equation in media with variations in c, ρ and v and its Pade (1,1) approximation are derived. The difference in numerical predictions of sound propagation in a stratified and turbulent atmosphere, based on the equation derived and ...