| 垂直激励圆柱形容器中的表面波特性研究 |
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| 引用本文： | 菅永军,鄂学全.垂直激励圆柱形容器中的表面波特性研究[J].应用力学学报,2004,21(1):5-12. |
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| 作者姓名： | 菅永军 鄂学全 |
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| 作者单位： | 1. 国家海洋局第一海洋研究所,青岛,266061;中国科学院力学研究所工程科学部,北京,100080
2. 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 ( 19772 0 63 ,19772 0 68) |
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| 摘 要： | 利用奇异摄动理论的两时间变量展开法，研究了垂直强迫激励圆柱形容器中的单一水表面驻波模式。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，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，并研究了特定(3，4)模式的表面驻波结构和特性，如驻波的节点分布及随某些参数的变化规律等，从计算的等高线的图象来看，和以往的实验结果相当吻合。
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| 关 键 词： | 奇异摄动理论 两时间变量展开法 表面驻波 垂直强迫振动 表面张力 流体力学 不稳定性 |
| 文章编号： | 1000-4939(2004)01-0005-08 |
Surface Wave Charicteristics in a Vertically Forced Circular Cylindrical Vessel |
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| Jian Yongjun,E Xuequan.Surface Wave Charicteristics in a Vertically Forced Circular Cylindrical Vessel[J].Chinese Journal of Applied Mechanics,2004,21(1):5-12. |
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| Authors: | Jian Yongjun E Xuequan |
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| Abstract: | This paper studys the single standing wave mode in a circular cylinder which is subjected to a vertical oscillation, employing two-time scales singular perturbation expansion. It is assumed that the fluid in circular cylindrical vessel is inviscid incompressible and the motion is irrotational. A dimensionless nonlinear evolution equation of slowly varying complex amplitude is derived without considering the effect of surface tension. The nonlinear amplitude equation is similar to a cubic nonlinear Schr dinger equation and incorporates the effect of parametric excitation. The standing surface wave's structures and characteristics of (3, 4) mode, such as the distribution of nodes and variable rules as the function of some parameters, is studied with the help of numerical computation. The contour of the free surface displacement agrees better with the results of experiment under the same condition. |
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| Keywords: | forced vertically oscillation nonlinear amplitude equation standing surface wave two-time scales expansion |
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