论文标题
粒子对扩散均匀的各向同性湍流的客观定量
Objective quantification of Particle Pair Diffusion in Homogeneous Isotropic Turbulence
论文作者
论文摘要
湍流包括相互作用的流量结构，这些流量结构涵盖了各种长度和时间尺度。一个长期存在的问题在近距离近端的颗粒对颗粒的扩散上笼罩，即粒子对在小分离处的扩散：湍流长度的范围尺度哪个范围控制对的扩散？在这里，我们试图通过通过精细尺度和较大尺度相干结构来解决嵌入精细尺度的较大规模结构的扩散来回答这个问题 - 我们不可避免地遇到了与小长度和大长度尺度相关的局部和非本地相互作用的组合。局部结构具有与对分离$ l $相同的数量级的长度尺度，并且它们在粒子对之间诱导强烈的相对运动。但是，具有长度尺度的非本地结构大于$ l $，也诱导（通过生物 - 萨瓦特）重要的相对运动，这在先前的研究中忽略了这种效果（基于Richardson-Obukhov R-O理论）。这从根本上改变了对扩散过程的解释，使得分散性$ k $缩放为$ k \ sim l^{1.556} $ - 在$ 1 \％的数据的$ 1 \％$内同意。 “ R-O常数” $ G_L $显示不变，尽管被广泛认为是常数。但是，确定了新常数（代表对扩散性$ g_k $和对分离$ g_l $），我们向渐近\ $ g_k \ osymptote显示了大约0.73 $和$ g_l \ sim \ sim 0.01 $在High Reynolds数字上。作为一种应用，我们表明，与R-O理论相比，喷雾剂云云在喷雾中的半径较小。
Turbulence consists of interacting flow structures covering a wide range of length and time scales. A long-standing question looms over pair diffusion of particles in close proximity i.e. particle pair diffusion at small separations: what range of turbulence length scales governs pair diffusion? Here, we attempt to answer this question by addressing pair diffusion by both fine scales and larger scale coherent structures in which the fine scales are embedded - we unavoidably encounter a combination of both local and non-local interactions associated with the small and large length scales. The local structures possess length scales of the same order of magnitude as the pair separation $l$, and they induce strong relative motion between the particle pair. However, the non-local structures, possessing length scales much larger than $l$, also induce (via Biot-Savart) significant relative motion, an effect ignored in prior studies (based on Richardson-Obukhov R-O theory). This fundamentally changes the interpretation of the pair diffusion process, giving the pair diffusivity $K$ scaling as $K\sim l^{1.556}$ -- agreeing within $1\%$ of data. The `R-O constant' $g_l$ is shown to be not a constant, although widely assumed to be a constant. However, new constants (representing pair diffusivity $G_K$ and pair separation $G_l$) are identified, which we show to asymptote to $G_K\approx 0.73$ and $G_l\sim 0.01$ at high Reynolds numbers. As an application, we show that the radius of a cloud of droplets in a spray is smaller by an order of magnitude as compared to R-O theory.
