论文标题
标量湍流中的小型各向同性和坡道裂口结构
Small-scale isotropy and ramp-cliff structures in scalar turbulence
论文作者
论文摘要
由三维Navier-Stokes湍流推高的被动标量在奇数矩中表现出基本异常，因为具有特征性的坡道裂解结构，违反了小型各向同性。我们使用直接数值模拟的数据，其网格分辨率高达$ 8192^3 $在高péclet数字上，以理解这种异常现象，因为标量扩散率，$ d $，减少或schmidt数字，$ sc =ν/d $，增加；这里$ν$是流体的运动粘度。微观雷诺数从140到650和$ sc $从1到512不等。显示出坡道裂口结构的简单模型显示出标量导数统计量的表征非常好。它准确地捕获了如何在较大的$ sc $限制中恢复小尺度的各向同性，并建议对批量长度尺度稍作校正为标量场中相关的最小比例。
Passive scalars advected by three-dimensional Navier-Stokes turbulence exhibit a fundamental anomaly in odd-order moments because of the characteristic ramp-cliff structures, violating small-scale isotropy. We use data from direct numerical simulations with grid resolution of up to $8192^3$ at high Péclet numbers to understand this anomaly as the scalar diffusivity, $D$, diminishes, or as the Schmidt number, $Sc = ν/D$, increases; here $ν$ is the kinematic viscosity of the fluid. The microscale Reynolds number varies from 140 to 650 and $Sc$ varies from 1 to 512. A simple model for the ramp-cliff structures is shown to characterize the scalar derivative statistics extremely well. It accurately captures how the small-scale isotropy is restored in the large-$Sc$ limit, and additionally suggests a slight correction to the Batchelor length scale as the relevant smallest scale in the scalar field.
