Numerical solution of the fourth moment equation for acoustic intensity correlations and comparison with the mid‐ocean acoustic transmission experiment

1996 ◽  
Vol 99 (3) ◽  
pp. 1419-1429 ◽  
Author(s):  
C. Macaskill ◽  
T. E. Ewart
Keyword(s):  
Numerical Solution ◽  
Moment Equation ◽  
Fourth Moment ◽  
Acoustic Transmission ◽  
Acoustic Intensity ◽  
Transmission Experiment

Numerical Solution of the Fourth-moment Equation for a Point Source

1990 ◽  
Vol 37 (5) ◽  
pp. 965-975 ◽  
Author(s):  
D.E. Reeve ◽  
S.R. Leonard ◽  
M. Spivack
Keyword(s):  
Point Source ◽  
Numerical Solution ◽  
Moment Equation ◽  
Fourth Moment

An improved solution to the fourth moment equation for intensity fluctuations

1983 ◽  
Vol 386 (1791) ◽  
pp. 461-474 ◽  
Keyword(s):  
High Frequency ◽  
Correction Term ◽  
Approximate Solutions ◽  
Moment Equation ◽  
Solution Procedure ◽  
Fourth Moment ◽  
Basic Solution ◽  
Numerical Work ◽  
First Order ◽  
First Order Correction

An approximate solution is presented for the fourth moment equation that describes fluctuations of intensity in a wave propagating through a randomly fluctuating medium. The solution is valid for high frequency or relatively strong fluctuations in the medium. The solution procedure is straightforward and at zero order agrees with previously derived approximate solutions. However, the present method is much more direct and more easily extended to complicated problems. Indeed, the first order correction to this basic solution is also determined and it is found that significantly better agreement with previous numerical work is obtained. In addition, knowledge of the correction term allows approximate estimates to be made for the error involved in using the basic solution.

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

1990 ◽  
Vol 37 (1) ◽  
pp. 5-12 ◽  
Author(s):  
S.R. Leonard ◽  
D.E. Reeve ◽  
M.C. Cook
Keyword(s):  
Grid Method ◽  
Moment Equation ◽  
Adaptive Grid ◽  
Fourth Moment

Underwater unidirectional acoustic transmission through a plate with bilateral asymmetric gratings

2018 ◽  
Vol 32 (11) ◽  
pp. 1850133 ◽  
Author(s):  
Ailing Song ◽  
Tianning Chen ◽  
Xiaopeng Wang ◽  
Yanhui Xi ◽  
Qingxuan Liang
Keyword(s):  
Displacement Field ◽  
Slit Width ◽  
Transmission Spectra ◽  
Acoustic Transmission ◽  
The Finite Element Method ◽  
Acoustic Intensity ◽  
Field Distributions ◽  
Intensity Field ◽  
Potential Applications ◽  
Ultrasonic Devices

In this paper, a novel underwater unidirectional acoustic transmission (UAT) device consisting of a plate with bilateral asymmetric gratings is proposed and numerically investigated. The transmission spectra, the acoustic intensity field distributions, and the displacement field distributions are numerically calculated based on the finite element method. The transmission spectra show that the proposed device exhibits different UAT effects in three bands. The acoustic intensity field distributions demonstrate that the proposed device can realize UAT, which agree well with the transmission spectra. The mechanism is discussed by analyzing the displacement field distributions, and the UAT is attributed to the symmetric mode excited in brass plate. Furthermore, the effects of the lattice constant, the upper slit width, and the lower slit width on bands are discussed. Our design provides a good reference for designing underwater UAT devices and has potential applications in some fields, such as medical ultrasonic devices, acoustic barrier, and noise insulation.

Simplification of an analytical solution of the fourth-moment equation

2004 ◽  
Vol 14 (2) ◽  
pp. 119-128
Author(s):  
Barry J Uscinski ◽  
G Campbell
Keyword(s):  
Analytical Solution ◽  
Moment Equation ◽  
Fourth Moment

Parabolic moment equations and acoustic propagation through internal waves

1980 ◽  
Vol 372 (1748) ◽  
pp. 117-148 ◽  
Keyword(s):  
Refractive Index ◽  
Frequency Spectrum ◽  
Autocorrelation Function ◽  
Internal Waves ◽  
Temporal Frequency ◽  
Acoustic Scattering ◽  
Moment Equation ◽  
Turbulent Medium ◽  
Fourth Moment ◽  
Moment Equations

Internal waves present in the ocean modulate its acoustic refractive index so that it behaves like a random weakly irregular medium with respect to an acoustic signal. The parabolic equations for the propagation of the moments of an acoustic wave are applied to this case to describe the random fluctuations of a sound wave in the ocean. A form of the GarrettMunk spectrum with a continuous range of vertical wavenumbers instead of a discrete set of mode numbers is used to describe the irregularities of refractive index due to internal waves and to obtain the transverse autocorrelation function that appears in the moment equations. This transverse autocorrelation function differs in several important aspects from that of a turbulent medium with ‘frozen’ irregularities advected with the medium. Some analytical solutions for the fourth and second moments are given. The solution of the fourth-moment equation is extended to give a new result: the temporal frequency spectrum of the intensity fluctuations This spectrum, which behaves like ω _1 in the region where the fluctuations, are large but not saturated, describes a feature common, under certain conditions, to optical and radio-wave scatter as well as to the acoustic case. The theory is compared with some experimental observations of acoustic scattering by internal waves where a frequency spectrum of this type first seems to have been observed.

Intensity fluctuations in a multiple scattering medium. Solution of the fourth moment equation

1982 ◽  
Vol 380 (1778) ◽  
pp. 137-169 ◽  
Keyword(s):  
Refractive Index ◽  
Spatial Frequency ◽  
Autocorrelation Function ◽  
Moment Equation ◽  
Scintillation Index ◽  
Fourth Moment ◽  
Scattering Medium ◽  
Frequency Spectra ◽  
Intensity Fluctuations ◽  
Limits Of Error

The intensity fluctuations arising when a wave propagates through a medium containing weak random inhomogeneities of refractive index are described by a parabolic equation for the fourth moment of the wave field. The present paper obtains an analytical solution for this equation when an initially plane wave is normally incident on a half-space containing such a medium. The solution is in the form of a multiple convolution and is valid even for multiple scatter. The multiple convolution is evaluated to yield an expression for the spatial frequency spectrum of intensity fluctuations. This spectrum is valid for any autocorrelation function of refractive index irregularities. Media with a Gaussian autocorrelation function and a Kolmogorov-type autocorrelation function of refractive index irregularities are treated as examples. Finally the spatial frequency spectra of intensity fluctuations are integrated to give the scintillation index curves as functions of distance of propagation in the medium. The regions of validity of the different approximations are discussed and the limits of error associated with the solutions are given.

A reciprocal acoustic transmission experiment for precise observations of tidal currents in a shallow sea

2021 ◽  
Vol 219 ◽  
pp. 108292
Author(s):  
Naokazu Taniguchi ◽  
Toshiyuki Takahashi ◽  
Kengo Yoshiki ◽  
Hironori Yamamoto ◽  
Aruni Dinan Hanifa ◽  
...  
Keyword(s):  
Tidal Currents ◽  
Acoustic Transmission ◽  
Shallow Sea ◽  
Transmission Experiment
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