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Updated: Aug 15, 2026
08:01
The Diffusion of Passive Tracers in Laminar Shear Flow
Published on: May 1, 2018
Dynamics of passive-scalar turbulence
Dhrubaditya Mitra1, Rahul Pandit
1Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India.
Physical Review Letters
|October 26, 2005
Summary
This study explores dynamic scaling in passive-scalar turbulence, finding simple scaling in the Kraichnan model but multiscaling only with multifractal velocity fields. Numerical simulations support these findings.
Area of Science:
- Turbulence Dynamics
- Statistical Physics
- Fluid Mechanics
Background:
- Passive-scalar turbulence describes how a non-active scalar field behaves within a turbulent flow.
- Understanding scaling properties is crucial for characterizing turbulent phenomena.
- Previous studies have focused on velocity field scaling, but scalar field dynamics remain less understood.
Purpose of the Study:
- To investigate the dynamic scaling and multiscaling behavior of passive-scalar turbulence.
- To determine the conditions under which simple scaling or multiscaling occurs.
- To analyze the influence of the advecting velocity field's properties on scalar turbulence.
Main Methods:
- Analytical derivations in Eulerian and quasi-Lagrangian frameworks for the Kraichnan model.
- Development and application of a multifractal model for passive-scalar turbulence.
- Numerical simulations using shell models to validate analytical predictions.
Main Results:
- Simple dynamic scaling is demonstrated for the Kraichnan version of passive-scalar turbulence.
- Different dynamic exponents are found for Eulerian and quasi-Lagrangian descriptions.
- Dynamic multiscaling is shown to occur if and only if the advecting velocity field is multifractal.
Conclusions:
- The study provides the first analysis of dynamic scaling and multiscaling in passive-scalar turbulence.
- The findings highlight the critical role of the advecting velocity field's multifractality in scalar turbulence.
- Results are robustly supported by both analytical methods and numerical simulations.
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