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Citation:
　Cunguo Xu,Zhan Wang,and Hayatdavoodi Masoud.Error Calculation of Large-Amplitude Internal Solitary Waves Within the Pycnocline Introduced by the Strong Stratification Approximation[J].Journal of Marine Science and Application,2023,(1):146-152.[doi:10.1007/s11804-023-00312-2]
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Error Calculation of Large-Amplitude Internal Solitary Waves Within the Pycnocline Introduced by the Strong Stratification Approximation

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Title:
Error Calculation of Large-Amplitude Internal Solitary Waves Within the Pycnocline Introduced by the Strong Stratification Approximation
Author(s):
Cunguo Xu1;  Zhan Wang1; 2; 3;  and Hayatdavoodi Masoud2; 4
Affilations:
Author(s):
Cunguo Xu1;  Zhan Wang1; 2; 3;  and Hayatdavoodi Masoud2; 4
1 Qingdao Innovation and Development Center of Harbin Engineering University, Qingdao 266555, China;
2 College of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, China;
3 Frontiers Science Center for Wave Field of Extreme Ocean Environment, Harbin Engineering University, Harbin 150001, China 4 Civil Engineering Department, School of Science and Engineering, University of Dundee, Dundee DD1 4HN, UK
Keywords:
Internal solitary wave|Pycnocline|Two-layer approximation|Three-layer approximation|MCC internal wave model|DJL equation|Wave profile|Wave speed
分类号:
-
DOI:
10.1007/s11804-023-00312-2
Abstract:
At present, studies on large-amplitude internal solitary waves mostly adopt strong stratification models, such as the twoand 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.

References:

Barros R, Choi W, Milewski PA (2020) Strongly nonlinear effects on internal solitary waves in three-layer flows. Journal of Fluid Mechanics 883:A16. https://doi.org/10.1017/jfm.2019.795
Camassa R, Choi W, Michallet H, Rus?s PO, Sveen JK (2006) On the realm of validity of strongly nonlinear asymptotic approxima-tions for internal waves. Journal of Fluid Mechanics 549:1-23.https://doi.org/10.1017/S0022112005007226
Camassa R, Tiron R (2011) Optimal two-layer approximation for continuous density stratification. Journal of Fluid Mechanics 669:32-54. DOI:10.1017/S0022112010004891
Cheng MH, Hsu JRC (2014) Effects of varying pycnocline thickness on interfacial wave generation and propagation. Ocean Engineering 88:34-45. https://doi.org/10.1016/j.oceaneng.2014.05.018
Choi W, Camassa R (1999) Fully nonlinear internal waves in a twofluid system. Journal of Fluid Mechanics 396:1-36. https://doi.org/10.1017/S0022112099005820
Cui J, Dong S, Wang Z (2021) Study on applicability of internal solitary wave theories by theoretical and numerical method. Applied Ocean Research 111:102629. https://doi.org/10.1016/j.apor.2021.102629
Du H, Wei G, Wang SD, Wang XL (2019) Experimental study of elevation- and depression-type internal solitary waves generated by gravity collapse. Physics of Fluids 31(10):102104. https://doi.org/10.1063/1.5121556
Dubreil-Jacotin ML (1934) Sur la détermination rigoureuse des ondes permanentes périodiques d’ampleur finie. Journal de Mathématiques Pures et Appliquées 13:217-291
Dunphy M, Subich C, Stastna M (2011) Spectral methods for internal waves:Indistinguishable density profiles and doublehumped solitary waves. Nonlinear Processes in Geophysics 18(3):351-358. https://doi.org/10.5194/npg-18-351-2011
Gao YX, You YX, Wang X, Li W (2012) Numerical simulation for the internal solitary wave based on MCC theory. Ocean Engineering 30(4):29-36. https://doi.org/10.16483/j.issn.1005-9865.2012.04.014
Gong Y, Xie J, Xu J, Chen Z, He Y (2022) Oceanic internal solitary waves at the Indonesian submarine wreckage site. Acta Oceano-logica Sinica 41(3):109-113. https://doi.org/10.1007/s13131-021-1893-0
Grue J, Jensen A, Rus?s PO, Sveen JK (1999) Properties of largeamplitude internal waves. Journal of Fluid Mechanics 380:257-278. https://doi.org/10.1017/S0022112098003528
Huang WH, You YX, Wang X, Hu TQ (2013) Wave-making experi-ments and theoretical models for internal solitary waves in a two-layer fluid of finite depth. Acta Physica Sinica 62(8):786-790. https://doi.org/10.7498/aps.62.084705
Huang X, Chen Z, Zhao W, Zhang Z, Zhou C, Yang Q, Tian J (2016) An extreme internal solitary wave event observed in the northern South China Sea. Scientific Reports 6(1):1-10. https://doi.org/10.1038/srep30041
Jo TC, Choi YK (2014) Dynamics of strongly nonlinear internal long waves in a three-layer fluid system. Ocean Science Journal 49(4):357-366. https://doi.org/10.1007/s12601-014-0033-6
Koop CG, Butler G (1981) An investigation of internal solitary waves in a two-fluid system. Journal of Fluid Mechanics 112:225-251. DOI:10.1017/S0022112081000372
Kuang GR (1986) The analysis of density and spring layer. Shan Dong Hai Yang Xue Bao (S1):60-73, 129. DOI:10.16441/j.cnki.hdxb.1986.s1.006. (in Chinese)
la Forgia G, Sciortino G (2019) The role of the free surface on interfacial solitary waves. Physics of Fluids 31(10):106601. https://doi.org/10.1063/1.5120621
la Forgia G, Sciortino G (2021) Free-surface effects induced by internal solitons forced by shearing currents. Physics of Fluids 33(7):072102. https://doi.org/10.1063/5.0055466
Long RR (1953) Some aspects of the flow of stratified fluids:I. A theoretical investigation. Tellus 5(1):42-58. https://doi.org/10.3402/tellusa.v5i1.8563
Lu H, Liu Y, Chen X, Zha G, Cai S (2021) Effects of westward shoaling pycnocline on characteristics and energetics of internal solitary wave in the Luzon Strait by numerical simulations. Acta Oceanologica Sinica 40(5):20-29. https://doi.org/10.1007/s13131-021-1808-0
Miyata M (1985) An internal solitary wave of large amplitude. La Mer 23(2):43-48
Miyata M (1988) Long internal waves of large amplitude. Horikawa, K., Maruo, H. (eds) Nonlinear Water Waves. International Union of Theoretical and Applied Mechanics. Springer, Berlin, Heidelberg.https://doi.org/10.1007/978-3-642-83331-1_44
Stastna M, Lamb KG (2002) Large fully nonlinear internal solitary waves:The effect of background current. Physics of Fluids 14(9):2987. https://doi.org/10.1063/1.1496510
Stastna M, Lamb KG (2020) An interesting oddity in the theory of large amplitude internal solitary waves. Russian Journal of Earth Sciences 20(4):5
Wang Z (2021) On the properties of ocean solitary waves with and without currents. PhD thesis, Harbin Engineering University, Harbin, 95-96
Xie J, Jian Y, Yang L (2010) Strongly nonlinear internal soliton load on a small vertical circular cylinder in two-layer fluids. Applied Mathematical Modelling 34(8):2089-2101. https://doi.org/10.1016/j.apm.2009.10.021
Zhang TY, Wang Z, Wang ZH, Xie BT, Zhao BB, Duan WY, Hayatdavoodi M (2020) On mode-1 and mode-2 internal solitary waves in a three-layer fluid system. Proceedings of the 35th International Workshop on Water Waves and Floating Bodies(IWWWFB), 173-176
Zou L, Ma XY, Li ZH (2020) Experimental reconstruction and flowfield analysis of stratified fluid soliton model. Journal of Harbin Engineering University 41(2):263-270. DOI:10.11990/jheu.2019 05113

Memo

Memo:
Received date:2022-10-3;Accepted date:2022-11-17。<br>Foundation item: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.<br>Corresponding author:Zhan Wang,E-mail:zhan.wang@hrbeu.edu.cn
Last Update: 2023-04-10