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Small-Scale Isotropy and Ramp-Cliff Structures in Scalar Turbulence
Dhawal Buaria1, Matthew P Clay2, Katepalli R Sreenivasan1,3
1Tandon School of Engineering, New York University, New York, New York 11201, USA.
Passive scalars in fluid turbulence show anomalies due to ramp-cliff structures. Increasing the Schmidt number (Sc) restores small-scale isotropy, as shown by direct numerical simulations.
Area of Science:
- Fluid dynamics
- Turbulence theory
- Statistical mechanics
Background:
- Passive scalars advected by turbulence exhibit anomalies in odd-order moments.
- Ramp-cliff structures in scalar fields violate small-scale isotropy.
Purpose of the Study:
- Investigate the anomaly in odd-order moments of passive scalars.
- Understand the role of scalar diffusivity (D) and Schmidt number (Sc) in restoring isotropy.
- Develop a model for ramp-cliff structures.
Main Methods:
- Direct numerical simulations of three-dimensional Navier-Stokes turbulence.
- Varying grid resolution up to 8192^3.
- Simulations at high Péclet numbers with Sc ranging from 1 to 512 and microscale Reynolds numbers from 140 to 650.
Main Results:
- A simple model for ramp-cliff structures accurately characterizes scalar derivative statistics.
- Small-scale isotropy is restored in the high Schmidt number (Sc) limit.
- The model suggests a correction to the Batchelor length scale.
Conclusions:
- Ramp-cliff structures are responsible for the fundamental anomaly in passive scalar moments.
- Increasing the Schmidt number is crucial for restoring small-scale isotropy in turbulent scalar fields.
- The developed model provides a quantitative description of scalar derivative statistics and offers insights into the smallest scales of the scalar field.
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