论文标题
在液体缸上雷利 - 柏拉图模式的动态稳定
Dynamic stabilisation of Rayleigh-Plateau modes on a liquid cylinder
论文作者
论文摘要
我们证明了轴对称傅立叶模式的动态稳定，易于通过径向振荡的体力对液体缸上经典的雷利 - 普拉托（RP）不稳定性。发现粘度在这种稳定中起着至关重要的作用。线性稳定性预测是通过Floquet分析获得的，表明RP不稳定模式可以使用径向强迫稳定。我们还解决了自由表面变形的线性粘性初始值问题，该方程获得了三维傅立叶模式的幅度。这个方程将概括在Patankar等人早些时候得出的圆柱体上控制法拉第波的Mathieu方程。 （2018年），时间非本地时间，代表其笛卡尔对应物的圆柱类似物（Beyer＆Friedrich 1995）。该方程式中的记忆项是物理上解释的，并且表明对于高粘性流体，其贡献可能很大。从数值解决方案到该方程的预测表明，RP模式稳定性高达几百个强迫循环，并且与不可压缩的Navier-Stokes方程的数值模拟非常吻合。
We demonstrate dynamic stabilisation of axisymmetric Fourier modes susceptible to the classical Rayleigh-Plateau (RP) instability on a liquid cylinder by subjecting it to a radial oscillatory body force. Viscosity is found to play a crucial role in this stabilisation. Linear stability predictions are obtained via Floquet analysis demonstrating that RP unstable modes can be stabilised using radial forcing. We also solve the linearised, viscous initial-value problem for free-surface deformation obtaining an equation governing the amplitude of a three-dimensional Fourier mode. This equation generalises the Mathieu equation governing Faraday waves on a cylinder derived earlier in Patankar et al. (2018), is non-local in time and represents the cylindrical analogue of its Cartesian counterpart (Beyer & Friedrich 1995). The memory term in this equation is physically interpreted and it is shown that for highly viscous fluids, its contribution can be sizeable. Predictions from the numerical solution to this equation demonstrates RP mode stabilisation upto several hundred forcing cycles and is in excellent agreement with numerical simulations of the incompressible, Navier-Stokes equations.
