Horizontal Refraction Effects of Sound Propagation Within Continental Shelf Slope Environment: Modeling and Theoretical Analysis
Horizontal refraction notably influences propagation characteristics with the variation of the waveguide environment. In this study, the horizontal refraction phenomenon at low frequencies was investigated in a sloping sea region with an incomplete vertical sound speed profile. Using the mode coupli...
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MDPI AG
2025-01-01
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| Series: | Journal of Marine Science and Engineering |
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| Online Access: | https://www.mdpi.com/2077-1312/13/2/217 |
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| author | Jinci Wang Bo Lei Yixin Yang Jianbo Zhou |
| author_facet | Jinci Wang Bo Lei Yixin Yang Jianbo Zhou |
| author_sort | Jinci Wang |
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| description | Horizontal refraction notably influences propagation characteristics with the variation of the waveguide environment. In this study, the horizontal refraction phenomenon at low frequencies was investigated in a sloping sea region with an incomplete vertical sound speed profile. Using the mode coupling theory, this research explores the relationship between horizontal refraction and energy exchange among modes, examining the impact of environmental conditions on the horizontal refraction angle. Theoretical derivations and numerical simulations reveal the mechanisms by which the source depth and modal order influence the horizontal refraction. The analysis indicates that the horizontal refraction angle increases with the modal order when the real part of the horizontal wavenumber <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>k</mi><mi>m</mi></msub></mrow></semantics></math></inline-formula> at the source position is less than the wavenumber <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>k</mi><mi>s</mi></msub></mrow></semantics></math></inline-formula>. In this situation, the horizontal refraction angle corresponding to the same modal order does not vary with the source depth. However, if the real part of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>k</mi><mi>m</mi></msub></mrow></semantics></math></inline-formula> is larger than <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>k</mi><mi>s</mi></msub></mrow></semantics></math></inline-formula>, then the horizontal refraction angle decreases as the source depth increases. This condition is due to the extremely small eigenfunction value at source depth of the low-order mode, thereby enhancing the mode coupling effect. The mode coupling is intimately associated with the mode excited by the source. Therefore, the source depth exerts a substantial influence on the horizontal refraction. Under these conditions, the modal order has a negligible effect on the horizontal refraction angle. |
| format | Article |
| id | doaj-art-91e5bd36ae1d483ea281eb61c0ee7e56 |
| institution | DOAJ |
| issn | 2077-1312 |
| language | English |
| publishDate | 2025-01-01 |
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| series | Journal of Marine Science and Engineering |
| spelling | doaj-art-91e5bd36ae1d483ea281eb61c0ee7e562025-08-20T02:44:53ZengMDPI AGJournal of Marine Science and Engineering2077-13122025-01-0113221710.3390/jmse13020217Horizontal Refraction Effects of Sound Propagation Within Continental Shelf Slope Environment: Modeling and Theoretical AnalysisJinci Wang0Bo Lei1Yixin Yang2Jianbo Zhou3School of Marine Science and Technology, Northwestern Polytechnical University, Xi’an 710072, ChinaSchool of Marine Science and Technology, Northwestern Polytechnical University, Xi’an 710072, ChinaSchool of Marine Science and Technology, Northwestern Polytechnical University, Xi’an 710072, ChinaSchool of Marine Science and Technology, Northwestern Polytechnical University, Xi’an 710072, ChinaHorizontal refraction notably influences propagation characteristics with the variation of the waveguide environment. In this study, the horizontal refraction phenomenon at low frequencies was investigated in a sloping sea region with an incomplete vertical sound speed profile. Using the mode coupling theory, this research explores the relationship between horizontal refraction and energy exchange among modes, examining the impact of environmental conditions on the horizontal refraction angle. Theoretical derivations and numerical simulations reveal the mechanisms by which the source depth and modal order influence the horizontal refraction. The analysis indicates that the horizontal refraction angle increases with the modal order when the real part of the horizontal wavenumber <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>k</mi><mi>m</mi></msub></mrow></semantics></math></inline-formula> at the source position is less than the wavenumber <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>k</mi><mi>s</mi></msub></mrow></semantics></math></inline-formula>. In this situation, the horizontal refraction angle corresponding to the same modal order does not vary with the source depth. However, if the real part of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>k</mi><mi>m</mi></msub></mrow></semantics></math></inline-formula> is larger than <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>k</mi><mi>s</mi></msub></mrow></semantics></math></inline-formula>, then the horizontal refraction angle decreases as the source depth increases. This condition is due to the extremely small eigenfunction value at source depth of the low-order mode, thereby enhancing the mode coupling effect. The mode coupling is intimately associated with the mode excited by the source. Therefore, the source depth exerts a substantial influence on the horizontal refraction. Under these conditions, the modal order has a negligible effect on the horizontal refraction angle.https://www.mdpi.com/2077-1312/13/2/217horizontal refractionmode couplingslope environmentvertical sound speed structure |
| spellingShingle | Jinci Wang Bo Lei Yixin Yang Jianbo Zhou Horizontal Refraction Effects of Sound Propagation Within Continental Shelf Slope Environment: Modeling and Theoretical Analysis Journal of Marine Science and Engineering horizontal refraction mode coupling slope environment vertical sound speed structure |
| title | Horizontal Refraction Effects of Sound Propagation Within Continental Shelf Slope Environment: Modeling and Theoretical Analysis |
| title_full | Horizontal Refraction Effects of Sound Propagation Within Continental Shelf Slope Environment: Modeling and Theoretical Analysis |
| title_fullStr | Horizontal Refraction Effects of Sound Propagation Within Continental Shelf Slope Environment: Modeling and Theoretical Analysis |
| title_full_unstemmed | Horizontal Refraction Effects of Sound Propagation Within Continental Shelf Slope Environment: Modeling and Theoretical Analysis |
| title_short | Horizontal Refraction Effects of Sound Propagation Within Continental Shelf Slope Environment: Modeling and Theoretical Analysis |
| title_sort | horizontal refraction effects of sound propagation within continental shelf slope environment modeling and theoretical analysis |
| topic | horizontal refraction mode coupling slope environment vertical sound speed structure |
| url | https://www.mdpi.com/2077-1312/13/2/217 |
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