Instability Analysis of Nonlinear Surface Waves in a Circular Cylindrical Container Subjected to a Vertical Excitation

doi:10.1016/j.euromechflu.2005.03.002

IMECH-IR > 力学所知识产出(1956-2008)

	Instability Analysis of Nonlinear Surface Waves in a Circular Cylindrical Container Subjected to a Vertical Excitation
	Jian YJ(菅永军); E XQ(鄂学全); Jian, YJ (reprint author), Chinese Acad Sci, Inst Mech, Beijing 100080, Peoples R China.
发表期刊	European Journal of Mechanics B-Fluids
	2005
卷号	24 期号:6 页码:683-702
ISSN	0997-7546
摘要	Singular perturbation theory of two-time scale expansions was developed both in inviscid and weak viscous fluids to investigate the motion of single surface standing wave in a liquid-filled circular cylindrical vessel, which is subject to a vertical periodical oscillation. Firstly, it is assumed that the fluid in the circular cylindrical vessel is inviscid, incompressible and the motion is irrotational, a nonlinear evolution equation of slowly varying complex amplitude, which incorporates cubic nonlinear term, external excitation and the influence of surface tension, was derived from solvability condition of high-order approximation. It shows that when forced frequency is low, the effect of surface tension on mode selection of surface wave is not important. However, when forced frequency is high, the influence of surface tension is significant, and can not be neglected. This proved that the surface tension has the function, which causes free surface returning to equilibrium location. Theoretical results much close to experimental results when the surface tension is considered. In fact, the damping will appear in actual physical system due to dissipation of viscosity of fluid. Based upon weakly viscous fluids assumption, the fluid field was divided into an outer potential flow region and an inner boundary layer region. A linear amplitude equation of slowly varying complex amplitude, which incorporates damping term and external excitation, was derived from linearized Navier-Stokes equation. The analytical expression of damping coefficient was determined and the relation between damping and other related parameters (such as viscosity, forced amplitude and depth of fluid) was presented. The nonlinear amplitude equation and a dispersion, which had been derived from the inviscid fluid approximation, were modified by adding linear damping. It was found that the modified results much reasonably close to experimental results. Moreover, the influence both of the surface tension and the weak viscosity on the mode formation was described by comparing theoretical and experimental results. The results show that when the forcing frequency is low, the viscosity of the fluid is prominent for the mode selection. However, when the forcing frequency is high, the surface tension of the fluid is prominent. Finally, instability of the surface wave is analyzed and properties of the solutions of the modified amplitude equation are determined together with phase-plane trajectories. A necessary condition of forming stable surface wave is obtained and unstable regions are illustrated. (c) 2005 Elsevier SAS. All rights reserved.
学科领域	力学
DOI	10.1016/j.euromechflu.2005.03.002
收录类别	SCI ; EI
语种	英语
WOS记录号	WOS:000233037700002
关键词[WOS]	FARADAY WAVES ; CYLINDER ; COMPETITION ; BASINS ; LIQUID ; CHAOS ; MODEL
WOS研究方向	Mechanics ; Physics
WOS类目	Mechanics ; Physics, Fluids & Plasmas
引用统计	被引频次：6[WOS] [WOS记录] [WOS相关记录]
文献类型	期刊论文
条目标识符	http://dspace.imech.ac.cn/handle/311007/16276
专题	力学所知识产出(1956-2008)
通讯作者	Jian, YJ (reprint author), Chinese Acad Sci, Inst Mech, Beijing 100080, Peoples R China.
推荐引用方式 GB/T 7714	Jian YJ,E XQ,Jian, YJ . Instability Analysis of Nonlinear Surface Waves in a Circular Cylindrical Container Subjected to a Vertical Excitation[J]. European Journal of Mechanics B-Fluids,2005,24,6,:683-702.
APA	菅永军,鄂学全,&Jian, YJ .(2005).Instability Analysis of Nonlinear Surface Waves in a Circular Cylindrical Container Subjected to a Vertical Excitation.European Journal of Mechanics B-Fluids,24(6),683-702.
MLA	菅永军,et al."Instability Analysis of Nonlinear Surface Waves in a Circular Cylindrical Container Subjected to a Vertical Excitation".European Journal of Mechanics B-Fluids 24.6(2005):683-702.

条目包含的文件		下载所有文件
文件名称/大小	文献类型	版本类型	开放类型	使用许可
94848.pdf（2292KB）			开放获取	--	浏览下载