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The Diffusion of Passive Tracers in Laminar Shear Flow
Published on: May 1, 2018
Heisenberg approximation in passive scalar turbulence
1Department of Physics, Indian Institute of Technology Guwahati, Guwahati 781039, India. kishore-dutta@iitg.ernet.in
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 9, 2011
Summary
This study derives analytic expressions for eddy viscosity and diffusivity using Heisenberg
Area of Science:
- Fluid Dynamics
- Turbulence Theory
- Statistical Mechanics
Background:
- Turbulence is characterized by complex energy and scalar transfer processes.
- Understanding universal constants in turbulence is crucial for theoretical and practical applications.
Purpose of the Study:
- Derive analytic expressions for eddy viscosity and diffusivity.
- Calculate universal turbulence constants: Batchelor (B), Kolmogorov (C), and turbulent Prandtl number (σ).
- Investigate the influence of space dimension (d) on these constants.
Main Methods:
- Heisenberg's approximation applied to Navier-Stokes and passive scalar dynamics.
- Evaluation of energy and mean-square scalar transfer integrals.
- Calculation of flux integrals and amplitude ratios.
- Analysis using two schemes: with and without ε expansion.
Main Results:
- Analytic expressions for eddy viscosity and diffusivity derived.
- Universal constants B, C, and σ calculated and compared with existing values.
- A new relation B = σC established.
- Behavior of constants with increasing space dimension analyzed, showing σ approaching 1 and B, C converging.
- Asymptotic relation B = B(0)d(1/3) derived for large dimensions.
Conclusions:
- The study provides a consistent theoretical framework for calculating key turbulence parameters.
- Results align with experimental and numerical findings, validating the approach.
- The derived relationships offer new insights into the dimensional dependence of turbulent transport properties.
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