Abstract
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.
Highlights
The Green’s function (GF) is the fundamental element in the acoustic calculation, which describes the sound field generated by a point source under certain boundary conditions or initial conditions, that is, the acoustic transfer relationship between the vibration source and the receiver is established
Theoretical Model of the Rigorous image source method (ISM) The theoretical foundation of the classical ISM for deriving the GF in the Pekeris waveguide is ray acoustics, where the sound field at any field point can be expressed as a superposition summation of the direct wave radiated by the sound source and the sound field reflected by the fluid–fluid interface [22]
An efficient GF for acoustic problems in shallow water was developed by the rigorous ISM model, in which the interaction between the spherical wave sound field and the liquid seabed of the Pekeris waveguide was established based on the classical ray theory and wave acoustics, and the sound loss due to multiple interactions with a lossy seabed was taken into account
Summary
The Green’s function (GF) is the fundamental element in the acoustic calculation, which describes the sound field generated by a point source under certain boundary conditions or initial conditions, that is, the acoustic transfer relationship between the vibration source and the receiver is established. For the liquid seabed, for example, the Pekeris waveguide, the reflection coefficient of a plane wave at the liquid–liquid interface is not always constant, and when there is sound absorption in the seabed medium, there can be no total reflection.
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