Turbulence is an ineffective mixer when Schmidt numbers are large

Dhawal Buaria, Matthew P. Clay, Katepalli R. Sreenivasan, P. K. Yeung

Published 2020-04-13Version 1

We solve the advection-diffusion equation for a stochastically stationary passive scalar $\theta$, 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 micro-scale Reynolds number varies in the range $140-650$ and the Schmidt number $Sc \equiv \nu/D$ in the range $1-512$, where $\nu$ is the kinematic viscosity of the fluid and $D$ is the molecular diffusivity of $\theta$. Our results show that turbulence becomes less effective as a mixer when $Sc$ is large. First, the mean scalar dissipation rate $\langle \chi \rangle = 2D \langle |\nabla \theta|^2\rangle$, when suitably non-dimensionalized, decreases as the inverse of $\log Sc$. Second, 1D cuts through the scalar field indicate increasing density of sharp fronts on larger scales, oscillating with large excursions and reduced mixing. The scaling exponents of the scalar structure functions in the inertial-convective range saturate with respect to the moment order and the saturation exponent approaches unity as $Sc$ increases, qualitatively consistent with 1D cuts of the scalar.