液滴触发的垂直强迫浴槽中的法拉第波
Droplet-triggered Faraday waves in a vertically forced bath
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中文总结 AI 辅助
本研究通过数值模拟揭示液滴反复撞击可在线性稳定浴槽中触发增长的法拉第波，识别出次谐波响应机制，并指出有限振幅扰动可低于线性阈值激发该动力学。
中文摘要 AI 辅助
在垂直强迫的浴槽中，液滴的反复撞击可以在强迫条件下产生增长的法拉第波响应，而在此条件下，相应的初始未扰动浴槽保持线性稳定。我们利用轴对称两相直接数值模拟，在广泛的雷诺数和韦伯数范围内研究这一机制。由此得到的现象学相图识别出准周期、衰减、微弱和不稳定浴槽响应。在我们考虑的参数路径上，向不稳定浴槽状态的转变发生在较窄的韦伯数范围内，并且随雷诺数变化较弱。在不稳定状态下，浴槽发展出以强迫频率一半的相干次谐波响应，而衰减状态中的扰动保持宽带并在连续反弹之间减弱。仅浴槽模拟表明，代表液滴撞击的有限振幅扰动可以激发受参数强迫限制的径向模式，从而在初始平坦浴槽的线性不稳定阈值以下启动增长的次谐波响应。一个简化的毛细主导模型提供了撞击等效扰动振幅的尺度估计，而用这些扰动初始化的仅浴槽模拟再现了耦合模拟中观察到的从有界到增长的转变。对有限圆柱浴槽的Floquet分析确定了第一个轴对称Neumann模式具有最低的次谐波不稳定阈值。时间分辨的Bessel分解独立地表明，增长的浴槽响应主要由相同的径向模式主导，而液滴诱导的次谐波响应主要投影到此结构上。这些结果确定了一条有限振幅路径，通过该路径，局部液滴撞击可以在初始未扰动浴槽的线性起始阈值以下进入法拉第波动力学。
英文摘要
Repeated impacts of a droplet on a vertically forced bath can produce a growing Faraday-wave response under forcing conditions for which the corresponding initially undisturbed bath remains linearly stable. We investigate this mechanism using axisymmetric two-phase direct numerical simulations over a wide range of Reynolds and Weber numbers. The resulting phenomenological regime map identifies quasi-periodic, decaying, faint, and unstable-bath responses. Along the parameter path considered here, the transition to the unstable-bath regime occurs over a narrow range of Weber numbers and varies only weakly with Reynolds number. In the unstable regime, the bath develops a coherent subharmonic response at half the forcing frequency, while disturbances in the decaying regime remain broadband and weaken between successive rebounds. Bath-only simulations show that a finite-amplitude perturbation representative of droplet impact can seed the confined radial mode susceptible to parametric forcing, initiating a growing subharmonic response below the linear instability threshold of the initially flat bath. A reduced capillary-dominated model provides a scaling estimate for the impact-equivalent perturbation amplitude, and bath-only simulations initialized with these perturbations reproduce the bounded-to-growing transition observed in the coupled simulations. Floquet analysis of the finite cylindrical bath identifies the first axisymmetric Neumann mode as having the lowest subharmonic instability threshold. A time-resolved Bessel decomposition independently shows that the growing bath response is dominated by the same radial mode, while the droplet-induced subharmonic response projects predominantly onto this structure. These results identify a finite-amplitude route by which localized droplet impacts can access Faraday-wave dynamics below the linear onset threshold of an initially undisturbed bath.
