Capillary Effect on the Vertically Excited Surface Wave in a Circular Cylindrical Vessel
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摘要: 在竖直振动的圆柱形容器中，利用理想流体中两时间尺度奇摄动展开法，研究了包括表面张力影响的自由面单一表面驻波的运动．通过求解势流方程，获得了一个包含三阶非线性项、外激励及表面张力影响的非线性振幅方程．结果表明当驱动频率较低时，表面张力对表面波模式选择不重要；然而，当驱动频率较高时，表面张力的影响是不可忽略的．说明表面张力具有使得自由面返回到平衡位置的作用．另外，由于考虑了表面张力的影响，使得理论结果比无表面张力时更加接近先前的实验结果．Abstract: In a vertically oscillating circular cylindrical container, singular perturbation theory of two-time scale expansions was developed in inviscid fluids to investigate the motion of single free surface standing wave including the effect of surface tension. A nonlinear slowly varying amplitude equation, which incorporates cubic nonlinear term, external excitation and the influence of surface tension, was derived from potential flow equation. The results show that when forced frequency is lower, the effect of surface tension on mode selection of surface wave is not important. However, when forced frequency is higher, the surface tension can not be neglected. This proved that the surface tension causes free surface returning to equilibrium location. In addition, due to considering the effect of surface tension, the theoretical result much more approaches to experimental results than that of no surface tension.
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