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在竖直振动的圆柱形容器中,将Navier_Stokes方程线性化,利用两时间尺度奇异摄动展开法研究了弱粘性流体的单一自由面驻波运动.整个流场被分为外部势流区和内部边界层区两部分,对两部分区域分别求解,得到包含阻尼项和外驱动影响的线性振幅方程.利用稳定性分析,得到形成稳定表面波的条件,给出了临界曲线.此外,还获得了阻尼系数的解析表达式.最后,将线性阻尼加到理想流体条件下所得到的色散关系中对其进行修正,理论结果证明修正后的驱动频率更加接近实验的结果.通过计算发现,当驱动的频率较低时,流体的粘性对表面波模式选择有重要影响,而表面张力的影响不明显;但当驱动频率较高时,流体的表面张力起主要作用,而流体的粘性影响甚小.
In a vertically vibrating cylindrical vessel, the Navier_Stokes equation is linearized, and the singular perturbation expansion method of two time scales is used to study the single free surface standing wave motion of the weakly viscous fluid. The whole flow field is divided into the external potential field and the internal The boundary layer of the two parts, the two parts of the region were solved, including the damping and the impact of external drive linear amplitude equation.Using the stability analysis, the formation of stable surface wave conditions, given the critical curve.Also obtained Finally, the linear damping is added to the dispersion relation obtained under the ideal fluid condition to correct it, and the theoretical result proves that the corrected driving frequency is closer to the experimental result.It is found through calculation that when the driven When the frequency is low, the viscosity of the fluid has an important influence on surface wave mode selection, but the surface tension has no obvious effect. However, when the driving frequency is high, the surface tension of the fluid plays a major role, while the viscosity of the fluid has little effect.