| 参数激励圆柱形容器中的非线性Faraday波 |
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| 引用本文： | 菅永军,鄂学全,柏威.参数激励圆柱形容器中的非线性Faraday波[J].应用数学和力学,2003,24(10):1057-1068. |
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| 作者姓名： | 菅永军 鄂学全 柏威 |
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| 作者单位： | 1.中国科学院, 力学研究所, 工程科学部, 北京, 100080; |
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| 基金项目： | 国家自然科学基金资助项目(19772063,19772068) |
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| 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。
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| 关 键 词： | 垂直强迫振动 非线性 Faraday波 奇异摄动展开 振幅方程 |
| 文章编号： | 1000-0887(2003)10-1057-12 |
| 收稿时间： | 2002-03-30 |
| 修稿时间： | 2002年3月30日 |
Nonlinear Faraday Waves in a Parametrically Excited Circular Cylindrical Container |
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| Institution: | 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 |
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| 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. |
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| Keywords: | vertically forced oscillation nonlinear Faraday wave singular perturbation expansion amplitude equation |
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