Effect of surface tension on the mode selection of vertically excited surface waves in a circular cylindrical vessel |
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| Authors: | Jian Yong-Jun E Xue-Quan Zhang Jie and Meng Jun-Min |
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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; Key Laboratory of Marine Science and Numerical Modelling, State Ocean Administration, Qingdao 266061, China |
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| 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. |
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| Keywords: | vertically forced oscillation nonlinear amplitude equation surface tension surface wave modes |
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