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Modelling nonlinear electrohydrodynamic surface waves over three-dimensional conducting fluids
Wang Z(王展); Wang, Z (reprint author), Chinese Acad Sci, Inst Mech, Key Lab Mech Fluid Solid Coupling Syst, Beijing 100190, Peoples R China.; Wang, Z (reprint author), Univ Chinese Acad Sci, Sch Engn Sci, Beijing 100049, Peoples R China.
Source PublicationPROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
2017-04-01
Volume473Issue:2200
ISSN1364-5021
AbstractThe evolution of the free surface of a three-dimensional conducting fluid in the presence of gravity, surface tension and vertical electric field due to parallel electrodes, is considered. Based on the analysis of the Dirichlet-Neumann operators, a series of fully nonlinear models is derived systematically from the Euler equations in the Hamiltonian framework without assumptions on competing length scales can therefore be applied to systems of arbitrary fluid depth and to disturbances with arbitrary wavelength. For special cases, well-known weakly nonlinear models in shallow and deep fluids can be generalized via introducing extra electric terms. It is shown that the electric field has a great impact on the physical system and can change the qualitative nature of the free surface: (i) when the separation distance between two electrodes is small compared with typical wavelength, the Boussinesq, Benney-Luke (BL) and Kadomtsev-Petviashvili (KP) equations with modified coefficients are obtained, and electric forces can turn KP-I to KP-II and vice versa; (ii) as the parallel electrodes are of large separation distance but the thickness of the liquid is much smaller than typical wavelength, we generalize the BL and KP equations by adding pseudo-differential operators resulting from the electric field; (iii) for a quasi-monochromatic plane wave in deep fluid, we derive the cubic nonlinear Schrodinger (NLS) equation, but its type (focusing or defocusing) is strongly influenced by the value of the electric parameter. For sufficient surface tension, numerical studies reveal that lump-type solutions exist in the aforementioned three regimes. Particularly, even when the associated NLS equation is defocusing for a wave train, lumps can exist in fully nonlinear models.
KeywordElectrohydrodynamics Lump Free-surface Wave
DOI10.1098/rspa.2016.0817
URL查看原文
Indexed BySCI ; EI
Language英语
WOS IDWOS:000408470700012
WOS KeywordSOLITARY WAVES ; ELECTRIC-FIELD ; WATER-WAVES ; INSTABILITY ; STABILITY ; EVOLUTION ; DYNAMICS ; EQUATION ; SHEETS
WOS Research AreaScience & Technology - Other Topics
WOS SubjectMultidisciplinary Sciences
Funding OrganizationStrategic Priority Research Program of the Chinese Academy of Sciences(XDB22040203) ; Key Research Program of Frontier Sciences, CAS(QYZDB-SSW-SYS015)
DepartmentLMFS水环境流体力学(LEM)
Classification二类
Ranking1
Citation statistics
Cited Times:3[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://dspace.imech.ac.cn/handle/311007/70046
Collection流固耦合系统力学重点实验室
Corresponding AuthorWang, Z (reprint author), Chinese Acad Sci, Inst Mech, Key Lab Mech Fluid Solid Coupling Syst, Beijing 100190, Peoples R China.; Wang, Z (reprint author), Univ Chinese Acad Sci, Sch Engn Sci, Beijing 100049, Peoples R China.
Recommended Citation
GB/T 7714
Wang Z,Wang, Z ,Wang, Z . Modelling nonlinear electrohydrodynamic surface waves over three-dimensional conducting fluids[J]. PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES,2017,473(2200).
APA 王展,Wang, Z ,&Wang, Z .(2017).Modelling nonlinear electrohydrodynamic surface waves over three-dimensional conducting fluids.PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES,473(2200).
MLA 王展,et al."Modelling nonlinear electrohydrodynamic surface waves over three-dimensional conducting fluids".PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES 473.2200(2017).
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