Abstract
At present, studies on large-amplitude internal solitary waves mostly adopt strong stratification models, such as the two-and three-layer Miyata—Choi—Camassa (MCC) internal wave models, which omit the pycnocline or treat it as another fluid layer with a constant density. Because the pycnocline exists in real oceans and cannot be omitted sometimes, the computational error of a large-amplitude internal solitary wave within the pycnocline introduced by the strong stratification approximation is unclear. In this study, the two- and three-layer MCC internal wave models are used to calculate the wave profile and wave speed of large-amplitude internal solitary waves. By comparing these results with the results provided by the Dubreil—Jacotin—Long (DJL) equation, which accurately describes large-amplitude internal solitary waves in a continuous density stratification, the computational errors of large-amplitude internal solitary waves at different pycnocline depths introduced by the strong stratification approximation are assessed. Although the pycnocline thicknesses are relatively large (accounting for 8%–10% of the total water depth), the error is much smaller under the three-layer approximation than under the two-layer approximation.
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27 January 2024
A Correction to this paper has been published: https://doi.org/10.1007/s11804-024-00402-9
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Funding
Supported by the Fundamental Research Funds for the Central Universities (No. 3072022FSC0101), the National Natural Science Foundation of China (Nos. 12202114, 52261135547), the China Postdoctoral Science Foundation (No. 2022M710932), the State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology (No. LP2202), the Qingdao Postdoctoral Application Project, and the Heilongjiang Touyan Innovation Team Program.
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Article Highlights
• The two- and three-layer MCC internal wave models and the DJL equation are used to study large-amplitude internal solitary waves.
• The error on profiles and speed of the internal solitary waves introduced by the strong stratification approximation are obtained.
• Three pycnocline thicknesses are considered to study the error of strong stratification approximation on describing internal solitary waves.
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Xu, C., Wang, Z. & Masoud, H. Error Calculation of Large-Amplitude Internal Solitary Waves Within the Pycnocline Introduced by the Strong Stratification Approximation. J. Marine. Sci. Appl. 22, 146–152 (2023). https://doi.org/10.1007/s11804-023-00312-2
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DOI: https://doi.org/10.1007/s11804-023-00312-2