Abstract
An exact approach is presented to compute the three-dimensional (3D) acoustic field in a homogeneous wedge-shaped ocean with perfectly reflecting boundaries. This approach applies the Fourier synthesis technique, which reduces a 3D point-source ideal wedge problem into a sequence of two-dimensional (2D) line-source ideal wedge problems, whose analytical solution is well established. A comparison of numerical efficiency is provided between this solution and the solution proposed by Buckingham, which is obtained by a sequence of integral transforms. The details of numerical implementation of these two solutions are also given. To validate the present approach and at the same time compare numerical efficiency between this approach and Buckingham’s analytical solution, two numerical examples are considered. One is the Acoustical Society of America (ASA) benchmark wedge problem and the other is a wide-angle wedge problem. Numerical results indicate that the present approach is efficient and capable of providing accurate 3D acoustic field results for arbitrary receiver locations, and hence can serve as a benchmark model for sound propagation in a homogeneous wedge-shaped ocean.
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References
Lee D, Botseas G, Siegmann W L. Examination of three-dimensional effects using a propagation model with azimuth-coupling capability (FOR3D). J Acoust Soc Am, 1992, 91: 3192–3202
Ballard M S. Modeling three-dimensional propagation in a continental shelf environment. J Acoust Soc Am, 2012, 131: 1969–1977
Fawcett J A, Dawson TW. Fourier synthesis of three-dimensional scattering in a two-dimensional oceanic waveguide using boundary integral equation methods. J Acoust Soc Am, 1990, 88: 1913–1920
Abawi A T, Kuperman W A, Collins M D. The coupled mode parabolic equation. J Acoust Soc Am, 1997, 102: 233–238
Perkins J S, Baer R N. An approximation to the three-dimensional parabolic-equation method for acoustic propagation. J Acoust Soc Am, 1982, 72: 515–522
Buckingham M J. Theory of acoustic radiation in corners with homogeneous and mixed perfectly reflecting boundaries. J Acoust Soc Am, 1989, 86: 2273–2291
Luo W Y, Schmidt H. Three-dimensional propagation and scattering around a conical seamount. J Acoust Soc Am, 2009, 125: 52–65
Buckingham M J. Theory of three-dimensional acoustic propagation in a wedgelike ocean with a penetrable bottom. J Acoust Soc Am, 1987, 82: 198–210
Buckingham M J, Tolstoy A. An analytical solution for benchmark problem 1: The “ideal” wedge. J Acoust Soc Am, 1990, 87: 1511–1513
Luo W Y, Yang C M, Qin J X, et al. Benchmark solutions for sound propagation in an ideal wedge. Chin Phys B, 2013, 22: 054301
Felsen L B. Numerical solutions of two benchmark problems. J Acoust Soc Am, 1987, 81: S39–S40
Deane G B, Buckingham M J. An analysis of the three-dimensional sound field in a penetrable wedge with a stratified fluid or elastic basement. J Acoust Soc Am, 1993, 93: 1319–1328
Jensen F B, Kuperman W A, Porter M B, et al. Computational Ocean Acoustics. 2nd ed. New York: Springer, 2011. 268–272
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Luo, W., Zhang, R. Exact solution of three-dimensional acoustic field in a wedge with perfectly reflecting boundaries. Sci. China Phys. Mech. Astron. 58, 594301 (2015). https://doi.org/10.1007/s11433-015-5691-6
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DOI: https://doi.org/10.1007/s11433-015-5691-6