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Three-dimensional Particle Tracking Velocimetry for Turbulence Applications: Case of a Jet Flow
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Steep Cliffs and Saturated Exponents in Three-Dimensional Scalar Turbulence
Kartik P Iyer1, Jörg Schumacher1,2, Katepalli R Sreenivasan1,3
1Tandon School of Engineering, New York University, New York, New York 11201, USA.
Physical Review Letters
|January 13, 2019
Summary
This study reveals that turbulent scalar intermittency, characterized by shocklike structures, exhibits scaling exponents that saturate at 1.2. This finding highlights a deep connection between geometry and statistics in turbulent mixing.
Area of Science:
- Fluid Dynamics
- Turbulence Research
- Scalar Transport
Background:
- Passive scalar intermittency in turbulent flows is a complex phenomenon.
- Understanding its statistical properties is crucial for various applications.
- Previous studies have suggested deviations from smooth, Gaussian statistics.
Purpose of the Study:
- To investigate the intermittency of a passive scalar in 3D Navier-Stokes turbulence.
- To provide unambiguous evidence for scaling exponent saturation.
- To explore the relationship between scalar field geometry and statistical properties.
Main Methods:
- Direct numerical simulations (DNS) on a 4096^3 grid.
- Analysis of high-order scalar increment moments.
- Calculation of fractal dimension for steep scalar cliffs.
Main Results:
- Scaling exponents for scalar increments saturate at 1.2 for high moment orders (>12).
- Scalar intermittency is dominated by singular, shocklike structures.
- Fractal dimension of steep cliffs is approximately 1.8, linking geometry and statistics (1.8 + 1.2 = 3).
- Anomalies in 4th and 6th order moments align with the Kraichnan model.
Conclusions:
- Scalar intermittency in this turbulent regime is governed by extreme events.
- A fundamental connection exists between the fractal geometry of scalar structures and their statistical scaling.
- The findings offer insights into turbulent mixing and scalar transport phenomena.
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