Bidirectional Whitham type equations for internal waves with variable topography

doi:10.1016/j.oceaneng.2022.111600

IMECH-IR > 流固耦合系统力学重点实验室

	Bidirectional Whitham type equations for internal waves with variable topography
	Yuan, Chunxin 1; Wang Z(王展)2,3,4
通讯作者	Wang, Zhan(zwang@imech.ac.cn)
发表期刊	OCEAN ENGINEERING
	2022-08-01
卷号	257 页码:12
ISSN	0029-8018
摘要	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.
关键词	Whitham type equations Bidirectional propagation Full dispersion Internal waves
DOI	10.1016/j.oceaneng.2022.111600
收录类别	SCI ; EI
语种	英语
WOS记录号	WOS:000812811500003
关键词[WOS]	SOLITARY WAVES ; WATER-WAVES ; NONLOCAL FORMULATION ; EVOLUTION-EQUATIONS ; MODEL ; LONG ; STABILITY ; AMPLITUDE ; SOLITONS ; STRAIT
WOS研究方向	Engineering ; Oceanography
WOS类目	Engineering, Marine ; Engineering, Civil ; Engineering, Ocean ; Oceanography
资助项目	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]
项目资助者	National Natural Science Foundation of China ; key program of the National Natural Science Foundation of China ; Natural Science Foundation of Shandong Province, China
论文分区	一类
力学所作者排名	1
RpAuthor	Wang, Zhan
引用统计
文献类型	期刊论文
条目标识符	http://dspace.imech.ac.cn/handle/311007/89692
专题	流固耦合系统力学重点实验室
作者单位	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
推荐引用方式 GB/T 7714	Yuan, Chunxin,Wang Z. Bidirectional Whitham type equations for internal waves with variable topography[J]. OCEAN ENGINEERING,2022,257:12.
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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