当Schmidt数较大时，Turbulence是无效混频器
Turbulence is an ineffective mixer when Schmidt numbers are large
摘要：
我们解决了对流扩散方程的随机静止被动标量$θ$，结合强制三维Navier-Stokes方程，使用直接数值模拟在不同大小的周期域，最大的是$8192^3$。泰勒尺度雷诺数在$140-650$范围内变化，施密特数$Sc \equiv ν/D$在$1-512$范围内变化，其中$ν$是流体的运动粘度，$D$是$θ$的分子扩散率。我们的研究结果表明，湍流成为一个无效的混合器时，$Sc$是大的。首先，当适当无量纲化时，平均标量耗散率$\langle χ\rangle = 2D \langle |\nabla θ|^2\rangle$减小为$1/\log Sc$。第二，一维削减通过标量场表明在更大的尺度上的尖锐的前沿密度增加，振荡与大的偏移导致减少混合，并另外建议削弱标量方差通量的规模。在惯性对流范围内的标量结构函数的标度指数出现饱和的时刻顺序和饱和指数接近统一的$Sc$增加，定性一致的一维削减的标量。
英文摘要：
We solve the advection-diffusion equation for a stochastically stationary passive scalar $θ$, in conjunction with forced 3D Navier-Stokes equations, using direct numerical simulations in periodic domains of various sizes, the largest being $8192^3$. The Taylor-scale Reynolds number varies in the range $140-650$ and the Schmidt number $Sc \equiv ν/D$ in the range $1-512$, where $ν$ is the kinematic viscosity of the fluid and $D$ is the molecular diffusivity of $θ$. Our results show that turbulence becomes an ineffective mixer when $Sc$ is large. First, the mean scalar dissipation rate $\langle χ\rangle = 2D \langle |\nabla θ|^2\rangle$, when suitably non-dimensionalized, decreases as $1/\log Sc$. Second, 1D cuts through the scalar field indicate increasing density of sharp fronts on larger scales, oscillating with large excursions leading to reduced mixing, and additionally suggesting weakening of scalar variance flux across the scales. The scaling exponents of the scalar structure functions in the inertial-convective range appear to saturate with respect to the moment order and the saturation exponent approaches unity as $Sc$ increases, qualitatively consistent with 1D cuts of the scalar.
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