标量turbulence中的小尺度各向同性和斜崖结构
Small-scale isotropy and ramp-cliff structures in scalar turbulence
摘要：
三维Navier-Stokes湍流平流的被动标量在奇阶矩中表现出基本的反常，这是由于其特征性的斜坡-悬崖结构，违反了小尺度各向同性。我们使用直接数值模拟的数据，网格分辨率高达$8192^3$在高Péclet数来理解这种异常的标量扩散，$D$，减少，或施密特数，$Sc = ν/D$，增加;这里$ν$是流体的运动粘度。微尺度雷诺数从140到650变化，$Sc$从1到512变化。斜坡悬崖结构的一个简单的模型示出的标量导数统计特性非常好。它准确地捕捉到小尺度各向同性如何在大$Sc$极限中恢复，并且另外建议对巴彻勒长度尺度作为标量场中的相关最小尺度进行轻微校正。
英文摘要：
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.
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