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

Abstract

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.

Wavelet-based cascade model for intermittent structure in terrestrial environments

“…Such a separation would require consideration of higher-order statistics. In Wilson et al (2008b), a relationship was found between the kurtosis and the packing fraction, for the case of turbulence. A more general equation could be derived and conceivably be used to separate φ 1 from q 2 1 .…”

“…Nonetheless, second-order statistics can provide very useful information on the spatial scales and distribution of object sizes in an RHM. Several previous papers (Goedecke et al, 2004(Goedecke et al, , 2006Wilson et al, 2009Wilson et al, , 2008b have derived correlation functions and spectra for the QW model. Here, we summarize some of these previous results.…”

A quasi-wavelet model for the turbulent refractive index

“…The probability distribution of the random variables used as building blocks for the QW representation is conveniently defined through the problem at hand. At first, we may consider N αn and R αn independent random variables, but a more detailed model of eddies interaction may require some dependence [10]. For the present discussion we will assume that the family of random variables {N αn } is Gaussian distributed.…”

“…Specifically, this model has successfully been employed in numerical simulations of atmospheric acoustics predicting wave scattering, outdoors sound propagation, and the forward problem of acoustic tomography [10]. Among its most important features, it is the capability to provide a virtually exact representation of any physically reasonable spectrum for passive scalar fluctuations.…”

Effect of randomly varying impedance on the interference of the direct and ground-reflected waves

“…The latter case can be treated with a concept of intermittency, similarly to that for sound propagation through an atmosphere with intermittent turbulence. 5 Thus, it seems worthwhile to study the effects of randomness in ground impedance on sound propagation. In the present paper, we will consider the classical problem of the sound field produced by a point source located above an impedance ground in a homogeneous atmosphere.…”