中国物理B ›› 2004, Vol. 13 ›› Issue (12): 2013-2020.doi: 10.1088/1009-1963/13/12/007

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Effect of surface tension on the mode selection of vertically excited surface waves in a circular cylindrical vessel

菅永军1, 张杰2, 孟俊敏2, 鄂学全3   

  1. (1)First Institute of Oceanography, State Oceanic Administration, Qingdao 266061, China; Institute of Mechanics, Chinese Academy of Sciences, Beijing 100080, China; (2)First Institute of Oceanography, State Oceanic Administration, Qingdao 266061, China; Key Laboratory of Marine Science and Numerical Modelling, State Ocean Administration, Qingdao 266061, China; (3)Institute of Mechanics, Chinese Academy of Sciences, Beijing 100080, China
  • 收稿日期:2003-11-27 修回日期:2004-07-27 出版日期:2004-12-17 发布日期:2005-03-17
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos 19772063, 19772068).

Effect of surface tension on the mode selection of vertically excited surface waves in a circular cylindrical vessel

Jian Yong-Jun (菅永军)ab, E Xue-Quan (鄂学全)b, Zhang Jie (张杰)ac, Meng Jun-Min (孟俊敏)ac    

  1. a First Institute of Oceanography, State Oceanic Administration, Qingdao 266061, Chinab Institute of Mechanics, Chinese Academy of Sciences, Beijing 100080, China; c  Key Laboratory of Marine Science and Numerical Modelling, State Ocean Administration, Qingdao 266061, China
  • Received:2003-11-27 Revised:2004-07-27 Online:2004-12-17 Published:2005-03-17
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos 19772063, 19772068).

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摘要： Singular perturbation theory of two-time-scale expansions was developed in inviscid fluids to investigate pattern-forming, structure of the single surface standing wave, and its evolution with time in a circular cylindrical vessel subject to a vertical oscillation. A nonlinear slowly varying complex amplitude equation, which involves a cubic nonlinear term, an external excitation and the influence of surface tension, was derived from the potential flow equation. Surface tension was introduced by the boundary condition of the free surface in an ideal and incompressible fluid. The results show that when forced frequency is low, the effect of surface tension on the mode selection of surface waves is not important. However, when the forced frequency is high, the surface tension cannot be neglected. This manifests that the function of surface tension is to cause the free surface to return to its equilibrium configuration. In addition, the effect of surface tension seems to make the theoretical results much closer to experimental results.

关键词: vertically forced oscillation, nonlinear amplitude equation, surface tension, surface wave modes

Abstract: Singular perturbation theory of two-time-scale expansions was developed in inviscid fluids to investigate pattern-forming, structure of the single surface standing wave, and its evolution with time in a circular cylindrical vessel subject to a vertical oscillation. A nonlinear slowly varying complex amplitude equation, which involves a cubic nonlinear term, an external excitation and the influence of surface tension, was derived from the potential flow equation. Surface tension was introduced by the boundary condition of the free surface in an ideal and incompressible fluid. The results show that when forced frequency is low, the effect of surface tension on the mode selection of surface waves is not important. However, when the forced frequency is high, the surface tension cannot be neglected. This manifests that the function of surface tension is to cause the free surface to return to its equilibrium configuration. In addition, the effect of surface tension seems to make the theoretical results much closer to experimental results.

Key words: vertically forced oscillation, nonlinear amplitude equation, surface tension, surface wave modes

中图分类号:  (Surface tension and related phenomena)

  • 68.03.Cd
02.30.-f (Function theory, analysis)