中国物理B ›› 2004, Vol. 13 ›› Issue (8): 1191-1200.doi: 10.1088/1009-1963/13/8/003

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Vertically forced surface wave in weakly viscous fluids bounded in a circular cylindrical vessel

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:2003-11-27 修回日期:2004-03-24 出版日期:2004-06-21 发布日期:2005-06-21
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos 19772063, 19772068).

Vertically forced surface wave in weakly viscous fluids bounded in a circular cylindrical vessel

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:2003-11-27 Revised:2004-03-24 Online:2004-06-21 Published:2005-06-21
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos 19772063, 19772068).

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摘要： Two-time scale perturbation expansions were developed in weakly viscous fluids to investigate surface wave motions by linearizing the Navier－Stokes equation in a circular cylindrical vessel which is subject to a vertical oscillation. The fluid field was divided into an outer potential flow region and an inner boundary layer region. A linear amplitude equation of slowly varying complex amplitude, which incorporates a damping term and external excitation, was derived for the weakly viscid fluids. The condition for the appearance of stable surface waves was obtained and the critical curve was determined. In addition, an analytical expression for the damping coefficient was determined and the relationship between damping and other related parameters (such as viscosity, forced amplitude, forced frequency and the depth of fluid, etc.) was presented. Finally, the influence both of the surface tension and the weak viscosity on the mode formation was described by comparing theoretical and experimental results. The results show that when the forcing frequency is low, the viscosity of the fluid is prominent for the mode selection. However, when the forcing frequency is high, the surface tension of the fluid is prominent.

关键词: vertically forced oscillation, weakly viscid fluid, surface wave modes, singular perturbation expansions, damping coefficient

Abstract: Two-time scale perturbation expansions were developed in weakly viscous fluids to investigate surface wave motions by linearizing the Navier－Stokes equation in a circular cylindrical vessel which is subject to a vertical oscillation. The fluid field was divided into an outer potential flow region and an inner boundary layer region. A linear amplitude equation of slowly varying complex amplitude, which incorporates a damping term and external excitation, was derived for the weakly viscid fluids. The condition for the appearance of stable surface waves was obtained and the critical curve was determined. In addition, an analytical expression for the damping coefficient was determined and the relationship between damping and other related parameters (such as viscosity, forced amplitude, forced frequency and the depth of fluid, etc.) was presented. Finally, the influence both of the surface tension and the weak viscosity on the mode formation was described by comparing theoretical and experimental results. The results show that when the forcing frequency is low, the viscosity of the fluid is prominent for the mode selection. However, when the forcing frequency is high, the surface tension of the fluid is prominent.

Key words: vertically forced oscillation, weakly viscid fluid, surface wave modes, singular perturbation expansions, damping coefficient

中图分类号:  (Hydrodynamic waves)

  • 47.35.-i
68.03.Cd (Surface tension and related phenomena)