论文标题
液滴碰撞中的分叉
Bifurcations in droplet collisions
论文作者
论文摘要
Saffman and Turner（1957）认为，随着湍流应变率的增加，湍流中液滴的碰撞速率会增加。但是Dhanasekaran等人的数值模拟。 （2021）在稳定的紧张流中表明，Saffman-Turner模型被过度简化，因为它忽略了液滴 - 滴滴的相互作用。这些导致碰撞速率对应变率和差分沉降速度的复杂依赖性。在这里，我们表明这种依赖性是通过碰撞动力学中的一系列分叉来解释的。当应变与重力对齐时，我们计算分叉图，并表明它对碰撞动力学产生了重要的见解。首先，稳态碰撞速率在极限kN $ \ to0 $中保持非零，这与普遍的假设是，碰撞速率在此极限下趋于零（KN是对空气平均空气平均自由路径的非二维度量）。其次，碰撞速率对差分沉降速度的非单调依赖性通过放牧分叉来解释。第三，分叉分析解释了为什么所谓的“封闭轨迹”出现并消失。第四，我们的分析预测在某些鞍点附近的强烈空间聚类，其中应变和差分定居的影响取消
Saffman and Turner (1957) argued that the collision rate for droplets in turbulence increases as the turbulent strain rate increases. But the numerical simulations of Dhanasekaran et al. (2021) in a steady straining flow show that the Saffman-Turner model is oversimplified because it neglects droplet-droplet interactions. These result in a complex dependence of the collision rate on the strain rate and on the differential settling speed. Here we show that this dependence is explained by a sequence of bifurcations in the collision dynamics. We compute the bifurcation diagram when strain is aligned with gravity, and show that it yields important insights into the collision dynamics. First, the steady-state collision rate remains non-zero in the limit Kn $\to0$, contrary to the common assumption that the collision rate tends to zero in this limit (Kn is a non-dimensional measure of the mean free path of air). Second, the non-monotonic dependence of the collision rate on the differential settling speed is explained by a grazing bifurcation. Third, the bifurcation analysis explains why so-called "closed trajectories" appear and disappear. Fourth, our analysis predicts strong spatial clustering near certain saddle points, where the effects of strain and differential settling cancel
