Turbulence is an Ineffective Mixer when Schmidt Numbers Are Large

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 periodic domains of various sizes, largest being $8192^3$. The Taylor-scale Reynolds number varies range $140-650$ and Schmidt $Sc \equiv \nu/D$ $1-512$, where $\nu$ is kinematic viscosity fluid $D$ molecular diffusivity $\theta$. Our results show that turbulence becomes an ineffective mixer when $Sc$ large. First, mean dissipation rate $\langle \chi \rangle = 2D \langle |\nabla \theta|^2\rangle$, suitably non-dimensionalized, decreases as $1/\log Sc$. Second, 1D cuts through field indicate increasing density sharp fronts on larger scales, oscillating large excursions leading to reduced mixing, additionally suggesting weakening variance flux across scales. scaling exponents structure functions inertial-convective appear saturate respect moment order saturation exponent approaches unity increases, qualitatively consistent scalar.