| Bidirectional Whitham type equations for internal waves with variable topography | |
Yuan, Chunxin1; Wang Z(王展)2,3,4
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| Corresponding Author | Wang, Zhan([email protected]) |
| Source Publication | OCEAN ENGINEERING
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| 2022-08-01 | |
| Volume | 257Pages:12 |
| ISSN | 0029-8018 |
| Abstract | In the context of oceanic internal gravity waves, one of the most widely-used theories on examining wave dynamics and interpreting observational data is the Korteweg-de Vries (KdV) equation. Nonetheless, the characters of unidirectional propagation and unbounded phase and group velocities restrict its application to some general cases (Benjamin et al., 1972). Thus, using the Dirichlet-Neumann operator with the rigid-lid approximation, we derive both bidirectional and unidirectional Whitham type equations in the Hamiltonian framework, which retain the full linear dispersion relation of the Euler equations. The effect of topography is also incorporated in modeling due to its practical relevance, although the invoked scaling plausibly excludes the accommodation of a significant bottom variation. There are no analytic solutions of internal solitary waves explicitly given in the newly proposed equations, even though these equations possess a concise form. Therefore, a modified Petviashvili iteration method is implemented to obtain the numerical solutions to circumvent this difficulty. Facilitated by these techniques, several numerical experiments are investigated and compared among different models: the KdV equation, the Whitham type equations, and the primitive equations. The discrepancies and similarities between the various models jointly indicate the advantage of full dispersion and bidirectional propagation and, thus, the effectiveness of the Whitham type equations. |
| Keyword | Whitham type equations Bidirectional propagation Full dispersion Internal waves |
| DOI | 10.1016/j.oceaneng.2022.111600 |
| Indexed By | SCI ; EI |
| Language | 英语 |
| WOS ID | WOS:000812811500003 |
| WOS Keyword | SOLITARY WAVES ; WATER-WAVES ; NONLOCAL FORMULATION ; EVOLUTION-EQUATIONS ; MODEL ; LONG ; STABILITY ; AMPLITUDE ; SOLITONS ; STRAIT |
| WOS Research Area | Engineering ; Oceanography |
| WOS Subject | Engineering, Marine ; Engineering, Civil ; Engineering, Ocean ; Oceanography |
| Funding Project | National Natural Science Foundation of China[11911530171] ; National Natural Science Foundation of China[11772341] ; National Natural Science Foundation of China[42006016] ; key program of the National Natural Science Foundation of China[12132018] ; key program of the National Natural Science Foundation of China[91958206] ; Natural Science Foundation of Shandong Province, China[ZR2020QD063] |
| Funding Organization | National Natural Science Foundation of China ; key program of the National Natural Science Foundation of China ; Natural Science Foundation of Shandong Province, China |
| Classification | 一类 |
| Ranking | 1 |
| Contributor | Wang, Zhan |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://dspace.imech.ac.cn/handle/311007/89692 |
| Collection | 流固耦合系统力学重点实验室 |
| Affiliation | 1.Ocean Univ China, Sch Math Sci, Songling 238 Rd, Qingdao 266100, Peoples R China; 2.Chinese Acad Sci, Inst Mech, Beijing 100190, Peoples R China; 3.Univ Chinese Acad Sci, Sch Engn Sci, Beijing 100049, Peoples R China; 4.Univ Chinese Acad Sci, Sch Future Technol, Beijing 100049, Peoples R China |
| Recommended Citation GB/T 7714 | Yuan, Chunxin,Wang Z. Bidirectional Whitham type equations for internal waves with variable topography[J]. OCEAN ENGINEERING,2022,257:12.Rp_Au:Wang, Zhan |
| APA | Yuan, Chunxin,&王展.(2022).Bidirectional Whitham type equations for internal waves with variable topography.OCEAN ENGINEERING,257,12. |
| MLA | Yuan, Chunxin,et al."Bidirectional Whitham type equations for internal waves with variable topography".OCEAN ENGINEERING 257(2022):12. |
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| Jp2022FA235_2022_Bid（1311KB） | 期刊论文 | 出版稿 | 开放获取 | CC BY-NC-SA | View Download | |
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