Ph. Blanc-Benon

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.

Misty Picture: A Unique Experiment for the Interpretation of the Infrasound Propagation from Large Explosive Sources

In the framework of the Comprehensive Nuclear-Test-Ban Treaty, the International Monitoring System develops a 60 micro-barometric stations network. These stations, which records infrasound, detect various powerful natural and artificial sources like long range explosions, oceanic swell, and volcano eruptions. For data analysis, the CEA, in collaboration with the LMFA, develops specific methods based on measurements, data processing and numerical simulation. The Misty Picture experiment is a high explosive event (4685 Tons of ANFO) realized in 1987 in New Mexico (US). Infrasounds were recorded by 22 sensors until a distance of 1000 km in a quiet background noise condition. Multi-reflected tropospheric, stratospheric and thermospheric phases are detected. Signals recorded near the source (1 km away) and observed in the geometrical shadow zone (between 150 km and 250 km from the point source) are of particular interest. This reference experiment very well documented is used to improve our understanding of the atmospheric propagation of infrasound as well as to evaluate our models. Using various methods such as ray tracing, parabolic equation and finite dierences, we investigate eects

Statistical moments of travel times at second order in isotropic and anisotropic random media

Abstract We study the high-frequency propagation of acoustic plane and spherical waves in random media. With the geometrical optics and the perturbation approach, we obtain the travel-time mean and travel-time variance at the second order. The main hypotheses are the Gaussian distribution of the acoustic speed perturbation and a factorized form for its correlation function. The second-order travel-time variance explains the nonlinear behaviour at large propagation distance observed with numerical experiments based on ray tracing. Usually, homogeneity and isotropy of the refractive index are considered. Using the geometrical anisotropy hypothesis we extend the theory to a general class of statistically anisotropic random media.

Parabolic equation for nonlinear acoustic wave propagation in inhomogeneous moving media

A new parabolic equation is derived to describe the propagation of nonlinear sound waves in inhomogeneous moving media. The equation accounts for diffraction, nonlinearity, absorption, scalar inhomogeneities (density and sound speed), and vectorial inhomogeneities (flow). A numerical algorithm employed earlier to solve the KZK equation is adapted to this more general case. A two-dimensional version of the algorithm is used to investigate the propagation of nonlinear periodic waves in media with random inhomogeneities. For the case of scalar inhomogeneities, including the case of a flow parallel to the wave propagation direction, a complex acoustic field structure with multiple caustics is obtained. Inclusion of the transverse component of vectorial random inhomogeneities has little effect on the acoustic field. However, when a uniform transverse flow is present, the field structure is shifted without changing its morphology. The impact of nonlinearity is twofold: it produces strong shock waves in focal regions, while, outside the caustics, it produces higher harmonics without any shocks. When the intensity is averaged across the beam propagating through a random medium, it evolves similarly to the intensity of a plane nonlinear wave, indicating that the transverse redistribution of acoustic energy gives no considerable contribution to nonlinear absorption.

Occurrence of Caustics for High Frequency Acoustic Waves Propagating Through Turbulent Fields

A numerical technique for simulating the propagation of high-frequency acoustic waves through turbulent fields is introduced. The technique involves two elements: the generation of a random isotropic scalar or vectorial field in terms of a superposition of discrete random Fourier modes; and the integration of the ray-trace equations of geometrical acoustics to describe the trajectories of rays and their distortion. For each realization we compute the ray trajectories and the evolution of the cross section of an elementary ray tube. We then accumulate statistics over an ensemble of realizations to estimate the probability of occurrence of the first caustic. Our results demonstrate that the position of caustics is governed by universal parameters related to the derivatives of the correlation function of the fluctuating components of the turbulent medium.

Nonlinear spherically divergent shock waves propagating in a relaxing medium

The propagation of nonlinear spherically diverging N-waves in atmosphere was studied experimentally and theoretically. The relative effects of nonlinear, dissipation, and relaxation phenomena on the N-wave duration and amplitude were investigated based on the numerical solutions of the modified Burgers equation. It is shown that, under the experimental conditions, the duration of a pulse increases mainly due to nonlinear propagation, whereas the amplitude depends on the combined effects of nonlinearity, dissipation, and relaxation. The frequency response of the measuring system is obtained. The calibration of the amplitude and duration of the experimental waveforms is performed based on the nonlinear lengthening of the propagating pulse. The results of numerical modeling show good agreement with experimental data.

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...

Toward an Improved Representation of Middle Atmospheric Dynamics Thanks to the ARISE Project

This paper reviews recent progress toward understanding the dynamics of the middle atmosphere in the framework of the Atmospheric Dynamics Research InfraStructure in Europe (ARISE) initiative. The middle atmosphere, integrating the stratosphere and mesosphere, is a crucial region which influences tropospheric weather and climate. Enhancing the understanding of middle atmosphere dynamics requires improved measurement of the propagation and breaking of planetary and gravity waves originating in the lowest levels of the atmosphere. Inter-comparison studies have shown large discrepancies between observations and models, especially during unresolved disturbances such as sudden stratospheric warmings for which model accuracy is poorer due to a lack of observational constraints. Correctly predicting the variability of the middle atmosphere can lead to improvements in tropospheric weather forecasts on timescales of weeks to season. The ARISE project integrates different station networks providing observations from ground to the lower thermosphere, including the infrasound system developed for the Comprehensive Nuclear-Test-Ban Treaty verification, the Lidar Network for the Detection of Atmospheric Composition Change, complementary meteor radars, wind radiometers, ionospheric sounders and satellites. This paper presents several examples which show how multi-instrument observations can provide a better description of the vertical dynamics structure of the middle atmosphere, especially during large disturbances such as gravity waves activity and stratospheric warming events. The paper then demonstrates the interest of ARISE data in data assimilation for weather forecasting and re-analyzes the determination of dynamics evolution with climate change and the monitoring of atmospheric extreme events which have an atmospheric signature, such as thunderstorms or volcanic eruptions.