中国物理B ›› 2004, Vol. 13 ›› Issue (10): 1631-1638.doi: 10.1088/1009-1963/13/10/009

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Instability of the vertically forced surface wave in a circular cylindrical container

菅永军1, 鄂学全2   

  1. (1)First Institute of Oceanography, State Oceanic Administration, Qingdao 266061, China; Institute of Mechanics, Chinese Academy of Sciences, Beijing 100080, China; (2)Institute of Mechanics, Chinese Academy of Sciences, Beijing 100080, China
  • 收稿日期:2003-12-02 修回日期:2004-05-25 出版日期:2004-10-20 发布日期:2005-06-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos 19772063, 19772068).

Instability of the vertically forced surface wave in a circular cylindrical container

Jian Yong-Jun (菅永军)ab, E Xue-Quan (鄂学全)b   

  1. a First Institute of Oceanography, State Oceanic Administration, Qingdao 266061, China; b Institute of Mechanics, Chinese Academy of Sciences, Beijing 100080, China
  • Received:2003-12-02 Revised:2004-05-25 Online:2004-10-20 Published:2005-06-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos 19772063, 19772068).

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摘要： The nonlinear amplitude equation, which was derived by Jian Yongjun employing expansion of two-time scales in inviscid fluids in a vertically oscillating circular cylindrical vessel, is modified by introducing a damping term due to the viscous dissipation of this system. Instability of the surface wave is analysed and properties of the solutions of the modified equation are determined together with phase-plane trajectories. A necessary condition of forming a stable surface wave is obtained and unstable regions are illustrated. Research results show that the stable pattern of surface wave will not lose its stability to an infinitesimal disturbance.

关键词: instability, vertically forced oscillation, amplitude equation, phase-plane trajectories

Abstract: The nonlinear amplitude equation, which was derived by Jian Yongjun employing expansion of two-time scales in inviscid fluids in a vertically oscillating circular cylindrical vessel, is modified by introducing a damping term due to the viscous dissipation of this system. Instability of the surface wave is analysed and properties of the solutions of the modified equation are determined together with phase-plane trajectories. A necessary condition of forming a stable surface wave is obtained and unstable regions are illustrated. Research results show that the stable pattern of surface wave will not lose its stability to an infinitesimal disturbance.

Key words: instability, vertically forced oscillation, amplitude equation, phase-plane trajectories

中图分类号:  (Hydrodynamic waves)

  • 47.35.-i
47.20.-k (Flow instabilities)