Turbulence is an Ineffective Mixer when Schmidt Numbers Are Large

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

Research output: Contribution to journalArticlepeer-review


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≡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 ⟨χ⟩=2D⟨|∇θ|^{2}⟩, when suitably nondimensionalized, decreases as 1/logSc. 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.

Original languageEnglish (US)
Article number074501
JournalPhysical Review Letters
Issue number7
StatePublished - Feb 19 2021

ASJC Scopus subject areas

  • General Physics and Astronomy


Dive into the research topics of 'Turbulence is an Ineffective Mixer when Schmidt Numbers Are Large'. Together they form a unique fingerprint.

Cite this