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Multiple-scale analysis and renormalization for preasymptotic scalar transport
A Mazzino1, S Musacchio, A Vulpiani
1INFM-Department of Physics, University of Genova, and INFN, Sezione di Genova, Via Dodecanneso 33, I-16146 Genova, Italy.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 9, 2005
Summary
This study investigates scalar transport in turbulent flows, developing a Fokker-Planck equation to model preasymptotic dynamics. The research highlights how diffusivity depends on large-scale velocity, confirmed by numerical simulations.
Area of Science:
- Fluid dynamics
- Statistical physics
- Turbulence research
Background:
- Scalar transport in complex flows is crucial in many scientific fields.
- Understanding preasymptotic dynamics, before statistical steady state, is challenging.
- Turbulent velocity fields with superimposed fluctuations complicate passive scalar advection.
Purpose of the Study:
- To analytically and numerically investigate the preasymptotic transport of a scalar quantity.
- To derive and analyze a Fokker-Planck equation for scalar dynamics under turbulent advection.
- To explore the dependence of effective diffusivity on the large-scale velocity component.
Main Methods:
- Multiple-scale expansion to derive a Fokker-Planck equation.
- Associated Langevin equation with multiplicative noise.
- Direct numerical simulations to validate analytical approximations.
Main Results:
- A Fokker-Planck equation accurately describes preasymptotic scalar dynamics.
- An approximation yields an explicit expression for effective diffusivity.
- Effective diffusivity is shown to explicitly depend on the large-scale advecting velocity.
Conclusions:
- The derived Fokker-Planck and Langevin equations provide a framework for preasymptotic scalar transport.
- The approximation for diffusivity is robust and validated by numerical simulations.
- The dependence of diffusivity on large-scale velocity is a key finding for turbulent transport.