论文标题
沿弱颗粒惯性处的Vieillefosse线形成湍流气溶胶中的苛性气
Caustics in turbulent aerosols form along the Vieillefosse line at weak particle inertia
论文作者
论文摘要
湍流气溶胶中颗粒空间分布的苛性奇异性提高了碰撞速率和加速凝结。在这里，我们通过分析在持续极限内的湍流气溶胶的三维高斯统计模型，研究弱颗粒惯性的苛性含量，与粒子松弛时间相比，该流动变化缓慢。在这种情况下，粒子和流体速度梯度之间的相关性很强，苛性剂量是由流体速度梯度的大型菌株主导的偏移引起的。这些游览必须越过由不变式$ q $和$ r $的流体速度梯度跨越的飞机上的特征阈值。我们的方法预测，达到此阈值的最可能方法是通过沿Vieillefosse线传播的唯一``最佳波动''，$ 27r^2/4 +q^3 = 0 $。我们确定最佳波动的形状是时间的函数，并表明它在数值统计模拟模拟中甚至对于中等粒子惯性而言是显着的。
Caustic singularities of the spatial distribution of particles in turbulent aerosols enhance collision rates and accelerate coagulation. Here we investigate how and where caustics form at weak particle inertia, by analysing a three-dimensional Gaussian statistical model for turbulent aerosols in the persistent limit, where the flow varies slowly compared with the particle relaxation time. In this case, correlations between particle- and fluid-velocity gradients are strong, and caustics are induced by large, strain-dominated excursions of the fluid-velocity gradients. These excursions must cross a characteristic threshold in the plane spanned by the invariants $Q$ and $R$ of the fluid-velocity gradients. Our method predicts that the most likely way to reach this threshold is by a unique ``optimal fluctuation'' that propagates along the Vieillefosse line, $27R^2/4 +Q^3=0$. We determine the shape of the optimal fluctuation as a function of time and show that it is dominant in numerical statistical-model simulations even for moderate particle inertia.
