参数激励圆柱形容器中的非线性Faraday波

菅永军; 鄂学全; 柏威

参数激励圆柱形容器中的非线性Faraday波

1.
中国科学院, 力学研究所, 工程科学部, 北京, 100080;
2.
国家海洋局, 第一海洋研究所, 山东, 青岛, 266061

基金项目: 国家自然科学基金资助项目(19772063,19772068)

详细信息

作者简介:
菅永军(1974- ),男,内蒙古巴彦淖尔盟人,博士(E-mail:jianyongjun@yahoo.com.cn).

中图分类号: O353.2
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- 被引次数: 0
出版历程
- 收稿日期: 2002-03-30
- 修回日期: 2003-05-16
- 刊出日期: 2003-10-15

Nonlinear Faraday Waves in a Parametrically Excited Circular Cylindrical Container

1.
Department of Engineering Science, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100080, P.R.China;
2.
First Institute of Oceanography, State Oceanic Administration, Qingdao, Shangdong 266061, P.R.China

摘要

摘要: 在柱坐标系下,通过奇异摄动理论的多尺度展开法求解势流方程,研究了垂直强迫激励圆柱形容器中的单一模式水表面驻波模式。假设流体是无粘、不可压且运动是无旋的,在忽略了表面张力的影响下,用两变量时间展开法得到一个具有立方项以及底部驱动项影响的非线性振幅方程。对上述方程进行了数值计算,计算的结果显示了在不同驱动振幅和驱动频率下,会激发不同自由水表面驻波模式,从等高线的图像来看,和以往的实验结果相当吻合。
- 垂直强迫振动 /
- 非线性 /
- Faraday波 /
- 奇异摄动展开 /
- 振幅方程
Abstract: In the cylindrical coordinate system,a singular perturbation theory of multiple-scale asymptotic expansions was developed to study single standing water wave mode by solving potential equations of water waves in a rigid circular cylinder,which is subject to a vertical oscillation.It is assumed that the fluid in the circular cylindrical vessel is inviscid,incompressible and the motion is irrotational, a nonlinear amplitude equation with cubic and vertically excited terms of the vessel was derived by expansion of two-time scales without considering the effect of surface tension.It is shown by numerical computation that different free surface standing wave patterns will be formed in different excited frequencies and amplitudes.The contours of free surface waves are agreed well with the experimental results which were carried out several years ago.
- vertically forced oscillation /
- nonlinear /
- Faraday wave /
- singular perturbation expansion /
- amplitude equation

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参考文献(17)

[1]	Faraday M. On the forms and states assumed by fluids in contact with vibrating elastic surfaces [J].Phil Trans R Soc Lond, 1831,121: 319-340.
[2]	Benjamin T B, Ursell F. The stability of the plane free surface of a liquid in vertical periodic motion [J]. Proc R Soc Lond A, 1954,255: 505-515.
[3]	Miles J W. Nonlinear surface wave in closed basins [J]. J Fluid Mech, 1976,75:419-448.
[4]	Meron E, Procaccia I. Low dimensional chaos in surface waves: Theoretical analysis of an experiment [J]. Phys Rev A, 1986,34: 3221-3237.
[5]	Larrza A, Putterman S. Theory of non-propagating surface solitons[J]. J Fluid Mech, 1984,148:443-449.
[6]	周显初.非传播孤立波和表面张力[J].力学学报,1998,30(6):672-675.
[7]	Miles J W. Nonlinear Faraday resonance [J]. J Fluid Mech, 1984, 83: 153-158.
[8]	Miles J W. Parametrically excited solitary waves [J]. J Fluid Mech, 1984,148: 451-460.
[9]	E Xue-quan, GAO Yu-xin. Ordered and chaotic modes of surface wave patterns in a vertically oscillating fluid [J]. Communications in Nonlinear Sciences & Numerical Simulation, 1996,1(2): 1-6.
[10]	E Xue-quan, GAO Yu-xin. Visualization of surface wave patterns of a fluid in vertical vibration [A].In: Proceedings of the Fourth Asian Symposium on Visualization[C]. 1996, Beijing, 653-658.
[11]	高宇欣,鄂学全.微幅振荡流体表面波图谱显示方法[J].实验力学,1998,13(3):326-333.
[12]	Ciliberto S, Gollub J P. Chaotic mode competition in parametrically forced surface waves [J]. J Fluid Mech, 1985,158: 381-398.
[13]	Nayfeh A H. Surface waves in closed basins under parametric and internal resonances [J]. Phys Fluids, 1987, 30: 2976-2983.
[14]	Feng Z C, Sethna P R. Symmetry-breaking bifurcations in resonant surface waves [J]. J Fluid Mech, 1989, 199: 495-518.
[15]	Nagata M. Nonlinear Faraday resonance in a box with a square base [J]. JFluid Mech, 1989,209:265-284.
[16]	Edwards W S, Fauve S. Patterns and quasi-patterns in the Faraday experiment [J]. JFluidMech,1994,278: 123-148.
[17]	Umeki M, Kambe T. Nonlinear dynamics and chaos in parametrically excited surface waves [J]. J Phys Soc Japan, 1989,58: 140-154.