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Stream-function solution of a two-layer Boussinesq model
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Rui LIANG1, Zhong-bo LIU1, Ke-zhao FANG2, Jia-wen SUN2, 3, Ping WANG2, 3
Journal of Ship Mechanics | 2025, 29(12) : 1874 - 1884
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Journal of Ship Mechanics | 2025, 29(12): 1874-1884
• Hydrodynamics •
Stream-function solution of a two-layer Boussinesq model
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Rui LIANG1, Zhong-bo LIU1, Ke-zhao FANG2, Jia-wen SUN2, 3, Ping WANG2, 3
Affiliations
  • 1.College of Transportation Engineering, Dalian Maritime University, Dalian 116026, China
  • 2.State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116024, China
  • 3.State Environmental Protection Key Laboratory of Marine Ecological Environment Restoration, National Marine Environmental Monitoring Center, Dalian 116023, China
Published: 2025-12-15 doi: 10.3969/j.issn.1007-7294.2025.12.005
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The Boussinesq model is a kind of wave model widely used in near-shore engineering, and its computational accuracy mainly depends on the basic performance of the model, while the upper bound of nonlinear application of the model has always been the focus of attention. In recent years, the two-layer Boussinesq model has gained great progress regarding theoretical properties, numerical modeling and applications. However, the value of its nonlinear upper bound has not been given in any literature. So in this study, the stream-function of the two-layer Boussinesq model was solved using a combination of genetic algorithm and Newton's method to determine the upper bound value of the model, considering the highest spatial derivatives of order 3 and 5. In the same way, the stream-function solutions of the corresponding one-layer Boussinesq model were derived. The numerical results show that the nonlinear upper bounds of the two-layer Boussinesq model with the highest derivatives of order 3 and 5 are H/L = 0.137 and 0.138. Compared with the one-layer Boussinesq model, the two-layer model has a greater water depth of applicability regarding strong nonlinear characteristics. The combination of genetic algorithm and Newton's method proposed in this study can provide some references for solving the stream-function waves of the related Boussinesq models.

Boussinesq model  /  stream-function  /  nonlinear upper bound  /  genetic algorithm  /  Newton’s method
Rui LIANG, Zhong-bo LIU, Ke-zhao FANG, Jia-wen SUN, Ping WANG. Stream-function solution of a two-layer Boussinesq model[J]. Journal of Ship Mechanics, 2025 , 29 (12) : 1874 -1884 . DOI: 10.3969/j.issn.1007-7294.2025.12.005
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Year 2025 volume 29 Issue 12
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doi: 10.3969/j.issn.1007-7294.2025.12.005
  • Receive Date：2025-06-15
  • Online Date：2026-07-07
  • Published：2025-12-15
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  • Received：2025-06-15
Affiliations
    1.College of Transportation Engineering, Dalian Maritime University, Dalian 116026, China
    2.State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116024, China
    3.State Environmental Protection Key Laboratory of Marine Ecological Environment Restoration, National Marine Environmental Monitoring Center, Dalian 116023, China
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https://castjournals.cast.org.cn/joweb/cblx/EN/10.3969/j.issn.1007-7294.2025.12.005
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表12种不同金属材料的力学参数
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Number of
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Number of
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鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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