Fourth Moment of a Wave Propagating in a Random Medium*

Brown, W. P.

doi:10.1364/josa.62.000966

Cited by 63 publications

(23 citation statements)

References 7 publications

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“…For an unbounded medium, the fourth moment equation was first solved numerically by Dagkesamanskayaand Shishov (1970), Brown (1972) and then by Tur (1982Tur ( , 1985 using finite difference techniques on a fixed grid. Encouraging agreement with approximate analytical solutions was reported for atmospheric propagation in Gozani (1985).…”

Section: Since the Parabolic Equation Is Identical To The Schrodingermentioning

confidence: 99%

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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Section: Since the Parabolic Equation Is Identical To The Schrodingermentioning

confidence: 99%

Sound through the internal wave field

Henyey

Macaskill

1996

Stochastic Modelling in Physical Oceanography

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“…The fourth moment of a wave field, E(x, z), with wavenumber k, propagating in the positive-z direction, is written as where x, z are a Cartesian set of coordinates and angle brackets denote an ensemble average . For a plane wave, normally incident on the random medium, the fourth moment of the wavefield E(x, z) obeys the equation [5] mz = -im 4,,-2F [1 -…”

Section: The Fourth-moment Equationmentioning

confidence: 99%

“…In this paper we solve the parabolic fourth moment equation . In the past, various computational methods have been employed to obtain solutions of this equation [3][4][5], but they have not always been either very reliable or accurate . Recently an operator splitting method (OSM) for solving the fourth-moment equation has been described [6,7] .…”

Section: Introductionmentioning

confidence: 99%

Solution of the Fourth-moment Equation by an Adaptive Grid Method

Leonard

Reeve

Cook

1990

Journal of Modern Optics

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The parabolic fourth moment equation for a plane wave is integrated numerically using an adaptive grid algorithm . Results are compared with those from an accurate, but far less efficient, operator splitting method, and agree very closely . The adaptive approach has several advantages over current fixed grid methods . The primary one is that significant reductions in computer memory usage can be obtained without a concomitant increase in run time . It is also ideally suited for accurate integration of the fourth-moment equation for an extremely large range of values of both the scattering parameter, F, and the wave propagation distance .

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“…The scalar parabolic equation for the fourth-order moment has been derived by many authors using different methods [Shishov, 1968;Tatarski, 1969; Beran and Ho, 1969; Molyneux, 1971;Brown, 1972;Furutsu, 1972…”

Section: Fj= 9j-•i •I=(]i+•i)/2 (2)mentioning

confidence: 99%

Covariance of irradiance fluctuations propagating through a thin turbulent slab

Furuhama¹

1975

Radio Science

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Irradiance fluctuations of a plane wave propagating through a strongly refracting thin turbulent slab are treated. The parabolic wave equation of the fourth‐order moment of the field is solved by an operational method and the triple integral form of the solution is obtained. Numerical results of the variance function show the saturation effect and the values of the covariance are given for the under‐ and over‐saturation regions.

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Fourth Moment of a Wave Propagating in a Random Medium*

Cited by 63 publications

References 7 publications

Sound through the internal wave field

Sound through the internal wave field

Solution of the Fourth-moment Equation by an Adaptive Grid Method

Covariance of irradiance fluctuations propagating through a thin turbulent slab

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