D. Juve

Simulation of the propagation of an acoustic wave through a turbulent velocity field: A study of phase variance

A numerical technique for simulating the behavior of an acoustic wave propagating through a turbulent medium is introduced. The technique involves two elements: the generation of 3‐D, random, hypothetical, isotropic velocity fields in terms of a collection of discrete Fourier velocity modes; and the integration of the ray‐trace equations to describe the trajectories of points tagging an acoustic wave front. The propagation times for these points to travel fixed distances through each of an ensemble of random velocity fields are recorded, and the variance of travel time (or acoustic phase) over the ensemble is calculated. In numerical ray‐trace experiments through fields having average perturbation indices ≊0.01, acoustic travel‐time variances are obtained that have a higher‐order dependence on travel distance R than the classical Chernov prediction—a linear increase with R. The Chernov result is obtained, however, when the rays are confined to axial trajectories. Additional numerical experiments integrati...

A numerical model for sound propagation through a turbulent atmosphere near the ground

In this paper a series of numerical simulations of the effect of turbulence on the propagation of acoustic waves in the atmosphere are presented. First the technique of representing the turbulence as a set of realizations of a random field generated by a limited number of Fourier modes is described. Through each individual realization, the acoustic waves are propagated in a wide-angle parabolic approximation to obtain the sound-pressure level. Ensemble averaging is then performed to compute the statistical properties of the acoustic field: mean sound-pressure level, intensity fluctuations, and amplitude distributions. The method is applied first to a nonrefractive atmosphere, both in the presence of a rigid boundary and of an impedance ground, and then to an upward refractive atmosphere with an impedance ground. The model, which contains no adjustable parameters, is tested using the experimental data of Parkin and Scholes, Daigle, and Wiener and Keast. Good agreement between numerical simulations and experiments is obtained.

On the appearance of caustics for plane sound-wave propagation in moving random media

Abstract In this paper we derive expressions for the probability densities of the appearance of the first caustic for a plane sound wave propagating in moving random media. Our approach generalizes the previous work by White et al. and Klyatskin in the case of motionless media. It allows us to calculate analytically the probability density functions for two- and three-dimensional media and to express these functions in terms of the diffusion coefficient. Explicit equations are given for Gaussian and von Karman spectra of velocity fluctuations. If the random scalar or vectorial fluctuations of the medium have the same contribution to the refractive-index fluctuations, we demonstrate that in a moving medium caustics appear at shorter distances than in a non-moving one. The two-dimensional version of the theory is tested by numerical simulations in the case of velocity fluctuations with Gaussian spectra. Numerical results are in very good agreement with the theoretical predictions.

Intensity fluctuations of spherical acoustic waves propagating through thermal turbulence

The intensity fluctuations of acoustic waves that propagate through thermal turbulence are investigated under well controlled laboratory conditions. Two heated grids in air are placed horizontally in a large anechoic room and the mixing of the free convection plumes above them generates a homogeneous isotropic random thermal field. The spectrum of refractive index fluctuations is accurately described by a modified von Karman model which takes into account the entire spectrum of turbulence. Experimental data are obtained by varying both the frequency of the spherical wave and the distance of propagation. In this paper we concentrate on the variance of the normalized intensity fluctuations and on their probability distributions. These measurements cover all the regimes from weak scattering to strong scattering including the peak of the intensity variance. Experimental values of the scintillation index are compared with classical theoretical predictions and also with the results of recent numerical simulatio...

Dislocations in the wave front of acoustic waves propagating through thermal turbulent fields

Acoustic waves traversing a turbulent medium develop random changes in phase and amplitude. Here the wavefront distortions of a spherical wave that traverses a medium exhibiting temperature fluctuations are investigated under well controlled laboratory conditions. A heated grid in air is placed horizontally in a large anechoic room and the mixing of the free convected plumes above the grid generates an homogeneous isotropic thermal turbulent field. By varying the frequency of the ultrasonic source and the distance of propagation, all the regimes from weak scattering to strong scattering can be explored. The presentation will concentrate on the measurements of phase variations along a linear array of microphones. Measurements of these phase differences demonstrate the limitation of the Rytov’s method for remote sensing techniques due to the existence of phase jumps between neighboring elements of the array. Numerical simulations based on a wide‐angle parabolic equation are used to explain these rapid phase...

On the influence of turbulence modeling for atmospheric sound propagation

Incorporating random aspects in the numerical simulation of atmospheric sound propagation has led to a much better agreement between experiments and predictions. In particular, the turbulent scattering of sound into acoustic shadows had been demonstrated but some discrepancies still exist. In most of the numerical studies the fluctuations of the refractive index have been considered as scalar and characterized by a single length scale (Gaussian spectrum). However, sound propagation in the turbulent atmosphere is affected by quantities with different tensorial character and different scales. In this paper two possible ways of improving the simulations are investigated: by choosing a better spectral representation of the turbulence (von Karman instead of Gaussian form); by correctly taking into account the vectorial character of wind fluctuations. The turbulence is represented as a set of realizations of a random field generated by a limited number of scalar or vectorial random Fourier modes. Through each i...

Coherence Aspects of Acoustic Wave Transmission Through a Medium with Temperature Fluctuations

The statistical properties of an ultrasonic wave that traverses a medium exhibiting temperature fluctuations are investigated. A heated grid in air is utilized to simulate the random thermal pattern typical of atmospheric and marine environments. The effect of temperature fluctuations on the attenuation of the transmitted pressure field and its mutual coherence is examined.

Sound propagation through thermal turbulence near a convex surface

Making use of an acoustic analogy, we study the sound propagation above a convex surface, to simulate the propagation of sound in an upward‐refracting medium and to investigate the scattering of sound by turbulence into an acoustic shadow zone. An experimental study was achieved under well‐controlled laboratory conditions. A heated grid is placed horizontally in a large anechoic room and the mixing of the free convection plumes above the grid generates a homogeneous isotropic random thermal field. The convex surface is simulated by a vertical cylinder. Experimental data are obtained by varying both the frequency of the acoustic source and the distance of propagation. Measurements will be presented for a rigid convex surface. In this paper, we concentrate on the mean sound‐pressure levels and the intensity fluctuations. Experimental values will be compared with results of numerical simulations based on a wide‐angle parabolic code.

Sound propagation through time‐dependent random media

In recent years, several authors have studied the impact of turbulence on sound propagation through numerical simulations. Currently, these simulations model the turbulence using a frozen turbulence hypothesis and a random Fourier modes (RFM) technique, such that the turbulent fluctuation at any point in the medium (either scalar or vectorial in nature) is calculated from the sum of a limited number of time‐independent random Fourier modes. The RFM technique is quite easy to implement, and has been used to make accurate predictions of ensemble‐averaged sound‐pressure level for atmospheric propagation. In this paper, the extension of the RFM method to include simple time evolution of the fluctuations is presented. However, this method produces fields that do not satisfy the Navier–Stokes equations and thus cannot exhibit either the dynamics or the structures found in atmospheric boundary layer (ABL) turbulence. The desire to include ABL turbulence characteristics in simulations of atmospheric propagation h...

Experimental observation of sound propagation through thermal turbulence near a boundary

The statistical properties of an ultrasonic wave that traverses a medium exhibiting temperature fluctuations are investigated under well‐controlled laboratory conditions. A heated grid in air is placed horizontally in a large anechoic room and the mixing of the free convection plumes above the grid generates a homogeneous isotropic random thermal field. The spectrum of refractrive index fluctuations is accurately described by a modified von Karman model which takes into account the entire spectrum of turbulence. Experimental data are obtained by varying both the frequency of the acoustic source and the distance of propagation. Measurements will be presented for a rigid boundary and for a finite impedance boundary. In this paper, attention is concentrated on the mean sound pressure levels and the intensity fluctuations. Experimental values will be compared with results of numerical simulations based on a wide angle parabolic code. [P. Chevret et al., J. Acoust. Soc. Am. 100, 3587–3599 (1996)]. [Work suppor...