论文标题
非线性毛细管波中的Dimple，喷气机和自相似性
Dimple, jets and self-similarity in nonlinear capillary waves
论文作者
论文摘要
从塌陷腔中对凹痕和喷气形成的数值研究通常将初始腔形状建模为截短的球体，模仿爆发的气泡。在这项研究中，我们提出了一个仅包含非线性惯性和毛细管力的最小模型，该模型会产生来自倒塌的毛细血管波槽的酒窝和喷气机。该槽从最初的扰动中发展起来，它被选为线性化问题的特征模式。我们解释了凹痕形成的物理机理，并证明，对于中等陡峭的陡峭度，模拟中看到的尖锐的凹痕被此处开发的弱非线性理论很好地捕获。对于陡度>> 1，该机制是强烈的非线性扩散表面能量到许多模式中，而前体凹痕现在发展为急剧上升的射流。在这里，模拟揭示了一个新颖的局部窗口（在时空和时间上），其中射流在Inviscid Keller＆Miksis（1983）量表之后会发展自相似。对于线性化的毛细管波，我们将这种制度与第一类的自相似解决方案进行了类比。我们的第一个原则研究表明，在足够小的尺度，凹痕和喷气机上，由于毛细血管的聚焦，需要（非线性）惯性和毛细管贡献，没有粘性或重力干预。
Numerical studies of dimple and jet formation from a collapsing cavity often model the initial cavity shape as a truncated sphere, mimicking a bursting bubble. In this study, we present a minimal model containing only nonlinear inertial and capillary forces, which produces dimples and jets from a collapsing, capillary wave trough. The trough develops from an initial perturbation, chosen to be an eigen-mode to the linearised problem.We explain the physical mechanism of dimple formation and demonstrate that, for moderate steepness, the sharp dimple seen in simulations is well captured by the weakly nonlinear theory developed here. For steepness >> 1 the regime is strongly nonlinear spreading surface energy into many modes and the precursor dimple now develops into a sharply rising jet. Here, simulations reveal a novel localised window (in space and time) where the jet evolves self-similarly following inviscid Keller & Miksis (1983) scales. We develop an analogy of this regime to a self-similar solution of the first kind, for linearised, capillary waves. Our first principles study demonstrates that at sufficiently small scales, dimples and jets form due to radial focussing of capillary waves requiring (nonlinear) inertial and capillary contributions, sans viscous or gravitational interventions.
