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
a First Institute of Oceanography, State Oceanic Administration, Qingdao 266061, China; b Institute of Mechanics, Chinese Academy of Sciences, Beijing 100080, China
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.
Received: 02 December 2003
Revised: 25 May 2004
Accepted manuscript online:
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos 19772063, 19772068).
Cite this article:
Jian Yong-Jun (菅永军), E Xue-Quan (鄂学全) Instability of the vertically forced surface wave in a circular cylindrical container 2004 Chinese Physics 13 1631
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