Instability of the vertically forced surface wave in a circular cylindrical container |
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| Authors: | Jian Yong-Jun and E Xue-Quan |
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| Affiliation: | First Institute of Oceanography, State Oceanic Administration, Qingdao 266061, China; Institute of Mechanics, Chinese Academy of Sciences, Beijing 100080, China |
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| 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. |
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| Keywords: | instability vertically forced oscillation amplitude equation phase-plane trajectories |
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