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Turbulence is an Ineffective Mixer when Schmidt Numbers Are Large
Dhawal Buaria1, Matthew P Clay2, Katepalli R Sreenivasan1,3
1Tandon School of Engineering, New York University, New York, New York 11201, USA.
Physical Review Letters
|March 5, 2021
Summary
High Schmidt numbers reveal turbulence is an ineffective mixer. Scalar dissipation decreases with increasing Schmidt numbers, indicating reduced mixing efficiency in fluid dynamics simulations.
Area of Science:
- Fluid dynamics
- Turbulence research
- Scalar transport
Background:
- Understanding passive scalar transport in turbulent flows is crucial for various scientific and engineering applications.
- The interplay between turbulence and molecular diffusion governs mixing processes.
Purpose of the Study:
- To investigate the impact of high Schmidt numbers on the mixing efficiency of passive scalars in turbulent flows.
- To analyze the behavior of scalar dissipation and structure functions under varying turbulence and diffusivity conditions.
Main Methods:
- Direct numerical simulations of the 3D Navier-Stokes equations coupled with the advection-diffusion equation.
- Simulations were performed in large periodic domains (up to 8192^3) across a range of Taylor-scale Reynolds numbers (140-650) and Schmidt numbers (1-512).
Main Results:
- Turbulence becomes an ineffective mixer at high Schmidt numbers (Sc).
- The mean scalar dissipation rate non-dimensionalized by D decreases as 1/logSc.
- Analysis revealed increasing density of sharp scalar fronts, reduced mixing, and weakening scalar variance flux across scales at high Sc.
- Scalar structure function exponents saturate with moment order, approaching unity as Sc increases.
Conclusions:
- High Schmidt numbers significantly impair the mixing capabilities of turbulence.
- The observed phenomena suggest a breakdown of efficient scalar mixing as molecular diffusion becomes dominant over turbulent eddies.
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