论文标题
当Schmidt数字很大时，湍流是一种无效的混合器
Turbulence is an ineffective mixer when Schmidt numbers are large
论文作者
论文摘要
我们使用强迫3D Navier-Stokes方程的随机固定的被动标量$θ$解决了固定固定的被动标量$θ$，使用直接数值模拟在各种尺寸的周期性域中，最大的$ 8192^3 $。泰勒级雷诺数的数字在$ 140-650 $中变化，而Schmidt Number $ sc \equivν/d $在$ 1-512 $中，其中$ν$是流体的运动粘度，$ d $是$ $θ$的分子扩散性。我们的结果表明，当$ SC $大时，湍流成为无效的混合器。首先，平均标量耗散率$ \ langleχ\ rangle = 2d \ langle | \nablaθ|^2 \ rangle $，如果适当地非二等化，则减少为$ 1/\ log sc $。其次，通过标量场的1D切割表明，较大尺度上的锋利前部的密度增加，通过较大的偏移来振荡，导致混合减少，并表明跨尺度上标量差异较弱。标量结构的缩放指数在惯性界面范围内的功能似乎相对于矩顺序而饱和，而饱和指数随着$ SC $的增加而接近统一，与标量量的一维切割一致。
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.
