Near Field Representations of the Acoustic Green's Function in a Shallow Ocean with Fluid-Like Seabed

Abstract In this paper, the near-field approximation of the acoustic Green's function in a two-layer waveguide is constructed by using a variation of the method of Ahluwalia and Keller [Exact and asymptotic representations of the sound field in a stratified ocean, Springer, 1977]. The relation between the constructed multiple-scattering representation (suitable for near-field) and the Hankel transform representation (suitable for mid-range) is also discussed in this paper. The construction scheme presented in this paper can be generalized for an N-layer waveguide.

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A Green’s Function for Acoustic Problems in Pekeris Waveguide Using a Rigorous Image Source Method

Applied Sciences ◽

10.3390/app11062722 ◽

2021 ◽

Vol 11 (6) ◽

pp. 2722

Author(s):

Zhiwen Qian ◽

Dejiang Shang ◽

Yuan Hu ◽

Xinyang Xu ◽

Haihan Zhao ◽

...

Keyword(s):

Green’S Function ◽

Shallow Water ◽

Green's Function ◽

Plane Waves ◽

Spherical Wave ◽

Sound Field ◽

Efficient Computation ◽

Image Source ◽

Source Method ◽

Pekeris Waveguide

The Green’s function (GF) directly eases the efficient computation for acoustic radiation problems in shallow water with the use of the Helmholtz integral equation. The difficulty in solving the GF in shallow water lies in the need to consider the boundary effects. In this paper, a rigorous theoretical model of interactions between the spherical wave and the liquid boundary is established by Fourier transform. The accurate and adaptive GF for the acoustic problems in the Pekeris waveguide with lossy seabed is derived, which is based on the image source method (ISM) and wave acoustics. First, the spherical wave is decomposed into plane waves in different incident angles. Second, each plane wave is multiplied by the corresponding reflection coefficient to obtain the reflected sound field, and the field is superposed to obtain the reflected sound field of the spherical wave. Then, the sound field of all image sources and the physical source are summed to obtain the GF in the Pekeris waveguide. The results computed by this method are compared with the standard wavenumber integration method, which verifies the accuracy of the GF for the near- and far-field acoustic problems. The influence of seabed attenuation on modal interference patterns is analyzed.

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The breakdown of the linearized theory and the role of quadrupole sources in transonic rotor acoustics

Journal of Fluid Mechanics ◽

10.1017/s0022112091002537 ◽

1991 ◽

Vol 226 ◽

pp. 591-624 ◽

Cited By ~ 10

Author(s):

H. Ardavan

Keyword(s):

Green’S Function ◽

Green's Function ◽

Impulsive Noise ◽

Near Field ◽

Point Of View ◽

Rotating Frame ◽

Homogeneous Wave ◽

Linearized Theory ◽

Near Field Sound ◽

Rotor Acoustics

The retarded Green's function for the linearized version of the equation of the mixed type governing the potential flow around a rotating helicopter blade or a propeller (with no forward motion) is derived and is shown to constitute the unifying feature of the various existing approaches to rotor acoustics. This Green's function is then used to pinpoint the singularity predicted by the linearized theory of rotor acoustics which signals its experimentally confirmed breakdown in the transonic regime: the gradient of the near-field sound amplitude, associated with a linear flow which is steady in the blade-fixed rotating frame, diverges on the sonic cylinder at the dividing boundary between the subsonic and supersonic regions of the flow. Prom the point of view of the equivalent Cauchy problem for the homogeneous wave equation, this singularity is caused by the imposition of entirely non-characteristic initial data on a space—time hypersurface which, at its points of intersection with the sonic cylinder, is locally characteristic. It also emerges from the analysis presented that the acoustic discontinuities detected in the far zone are generated by the quadrupole source term in the Ffowcs Williams-Hawkings equation and that the impulsive noise resulting from these discontinuities would be removed if the flow in the transonic region were to be rendered unsteady (as viewed from the blade-fixed rotating frame).

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