Numerical solution for the fourth-order coherence function of a plane wave propagating in a two-dimensional Kolmogorovian medium

The analytical theory of the Global Navigation Satellite Systems (GNSS) signal propagation through the inhomogeneous ionosphere with time-varying embedded localized random inhomogeneities of electron density is constructed in order to describe the regime of strong scintillation of the wave field propagating in the inhomogeneous ionospheric layer. The theory is based on the solutions of the appropriate Markov's parabolic moment equations, extended to the case of the inhomogeneous background medium. The solutions are validated by the comparison with some rigorous (numerical) solutions known for some limiting cases. The developed theory forms the theoretical background for constructing the physically based software simulator of the random transionospheric GNSS signals.

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“…The Gozani's solution was constructed for the Kolmogorov power law of the refraction index fluctuations [ Gozani , , equation (2)].

D_{n} ((), ρ) = 2.91 C_{n}^{2} true| ρ true|^{\frac{5}{3}},

which agrees with our model ( and ).…”

Section: Numerical Resultssupporting

confidence: 68%

“…There, the dependence of S 4 is given as the function of the universal variable

η = {(C_{n}^{2} k^{7 / 6})}^{6 true/ 11} z

along the raypath. Variable η from is the same as used by Gozani []. The comparison is presented of this solution against the reference numerical solution.…”

Section: Numerical Resultsmentioning

confidence: 99%

Strong scintillation of GNSS signals in the inhomogeneous ionosphere: 1. Theoretical background

Zernov

Gherm

2015

Radio Sci.

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“…Encouraging agreement with approximate analytical solutions was reported for atmospheric propagation in Gozani (1985). Further progress was made when Spivack and Uscinski (1988) provided numerical solutions using a split-step Fourier technique on a fixed grid.…”

Section: Since the Parabolic Equation Is Identical To The Schrodingermentioning

confidence: 74%

Sound through the internal wave field

Henyey

Macaskill

1996

Stochastic Modelling in Physical Oceanography

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We review the subject of sound propagation through the random ocean internal wave field. Among the assumptions that are usually made, two are identified as not always valid: the Markov approximation and the expansion around a deterministic ray. When these approximations are valid, and the internal wave field known, acoustic phase :O.uctuations are very accurately predicted and intensity :O.uctuations reasonably well calculated. For the calculations of statistical moments of the acoustic field, the two techniques of moment equations and path integrals have been developed to a high degree, and give similar results. Among all other statistical quantities, the probability density function for intensity has received the most attention, but no satisfactory theory has been developed for this or other quantities.

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“…Many approaches have been used to simulate the propagation of acoustic waves through random media. One may numerically solve the propagation equations for the statistical moments, e.g., the fourth order moment (e.g., Yeh et al, 1975;Tur, 1982;Gozani, 1985;Spivack and Uscinski, 1988). Another approach consists of simulating sound propagation through multiple realizations of "frozen" turbulence.…”

Section: Introductionmentioning

confidence: 99%

Evaluating a linearized Euler equations model for strong turbulence effects on sound propagation

Ehrhardt

Cheinet

Juvé

et al. 2013

The Journal of the Acoustical Society of America

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Sound propagation outdoors is strongly affected by atmospheric turbulence. Under strongly perturbed conditions or long propagation paths, the sound fluctuations reach their asymptotic behavior, e.g., the intensity variance progressively saturates. The present study evaluates the ability of a numerical propagation model based on the finite-difference time-domain solving of the linearized Euler equations in quantitatively reproducing the wave statistics under strong and saturated intensity fluctuations. It is the continuation of a previous study where weak intensity fluctuations were considered. The numerical propagation model is presented and tested with two-dimensional harmonic sound propagation over long paths and strong atmospheric perturbations. The results are compared to quantitative theoretical or numerical predictions available on the wave statistics, including the log-amplitude variance and the probability density functions of the complex acoustic pressure. The match is excellent for the evaluated source frequencies and all sound fluctuations strengths. Hence, this model captures these many aspects of strong atmospheric turbulence effects on sound propagation. Finally, the model results for the intensity probability density function are compared with a standard fit by a generalized gamma function.

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Numerical solution for the fourth-order coherence function of a plane wave propagating in a two-dimensional Kolmogorovian medium

Cited by 36 publications

References 10 publications

Strong scintillation of GNSS signals in the inhomogeneous ionosphere: 1. Theoretical background

Strong scintillation of GNSS signals in the inhomogeneous ionosphere: 1. Theoretical background

Sound through the internal wave field

Evaluating a linearized Euler equations model for strong turbulence effects on sound propagation

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