Professor LUO Wenyu and his group from the State Key Laboratory of Acoustics, Institute of Acoustics, Chinese Academy of Sciences, set out to tackle this problem. After several years of innovative research, they have developed an accurate, efficient, and numerically stable coupled normal mode method to solve the range-dependent propagation problem. Their work, entitled "A numerically stable coupled-mode formulation for acoustic propagation in range-dependent waveguides", was published in SCIENCE CHINA Physics, Mechanics & Astronomy. 2012, Vol. 55(4).
The source is located at a range of 4 km and a depth of 100 m by the: (a) analytical solution at 25 Hz; (b) present model at 25 Hz; (c) analytical solution at 100 Hz; (d) present model at 100 Hz. Credit: © Science China Press
Underwater sound propagation in range-dependent waveguides is critical to many studies and applications in the area of underwater acoustics. Neglect of waveguide range-dependence may lead to significant prediction errors. A number of approaches have been developed for solving this problem. Despite significant recent advances, problems such as intensive computation and instability remain unsolved. Therefore, the need for developing new approaches with better efficiency, stability, and accuracy is urgent.
In the method proposed by LUO et al., the direct global matrix (DGM) approach is applied. As is well-established, the primary advantage of the DGM approach is that it gives numerically stable solutions when there is evanescence across layers, and it does this without special numerical treatment. Therefore, the proposed method is unconditionally stable. Furthermore, by introducing appropriately normalized range solutions, the overflow problem inherent in certain existing models is eliminated. In addition, general source conditions were put forward, which significantly extends the applicability of the proposed model compared to existing models.
This research was partially supported by grants from the National Natural Science Foundation of China and the Knowledge Innovation Program of Chinese Academy of Sciences. The proposed method proves to be accurate, efficient, and numerically stable. The researchers suggest their work be extended and applied to the study of three-dimensional effects, for instance, the horizontal refraction that is present in complex environments. This will have significant impact on the study of three-dimensional underwater sound propagation.
See the article: Luo W Y, Yang C M, Qin J X, et al. A numerically stable coupled-mode formulation for acoustic propagation in range-dependent waveguides. SCIENCE CHINA Physics, Mechanics & Astronomy, 2012, 55(4): 572-588
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