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Magnetically Induced Rotating Rayleigh-Taylor Instability

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Small-Scale Isotropy and Ramp-Cliff Structures in Scalar Turbulence.

Dhawal Buaria¹, Matthew P Clay², Katepalli R Sreenivasan^1,3

¹Tandon School of Engineering, New York University, New York, New York 11201, USA.

Physical Review Letters

|February 5, 2021

Summary

This summary is machine-generated.

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.

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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.