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Drift-free kinetic equations for turbulent dispersion
A Bragg1, D C Swailes, R Skartlien
1Sibley School of Mechanical & Aerospace Engineering, Cornell University, Ithaca, New York 14853-7501, USA. adb265@cornell.edu
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 11, 2012
Summary
This study reveals that different kinetic equation formulations for turbulent dispersion are not equivalent. One specific kinetic equation accurately models dispersion in inhomogeneous turbulence, satisfying the zero-drift condition.
Area of Science:
- Fluid Dynamics
- Turbulence Research
- Statistical Mechanics
Background:
- Dispersion of passive scalars and inertial particles in turbulent flows is often modeled using probability density functions (PDFs).
- Transport equations, known as kinetic equations, govern the evolution of these PDFs.
- Existing literature widely assumes equivalence among various PDF kinetic equation formulations.
Purpose of the Study:
- To demonstrate that PDF kinetic equation formulations are not equivalent.
- To identify the most appropriate kinetic equation for modeling dispersion in inhomogeneous turbulence.
- To assess consistency with particle equations of motion and the zero-drift condition.
Main Methods:
- Analysis of PDF kinetic equations for inertial particles.
- Consideration of the zero particle Stokes number limit.
- Assessment against the fully mixed (zero-drift) condition for fluid points.
- Formal demonstration using the Furutsu-Novikov method.
Main Results:
- Significant differences exist among various PDF kinetic equation formulations.
- One kinetic equation formulation, derived via the Furutsu-Novikov method, precisely satisfies the zero-drift condition in both homogeneous and inhomogeneous turbulence.
- Other kinetic equation forms fail to meet this condition or are restricted to limited regimes.
Conclusions:
- The equivalence of PDF kinetic equations is a misconception.
- The Furutsu-Novikov derived kinetic equation is uniquely suitable for modeling dispersion in inhomogeneous turbulent flows.
- This validated kinetic equation resolves a long-standing question on the validity of kinetic equations in the fluid-point limit.
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