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Effect of helicity on the effective diffusivity for incompressible random flows
D S Dean1, I T Drummond, R R Horgan
1Laboratoire de Physique Quantique, l'Institut de Rechesche Sur les Systemes Atomiques et Moleculaires Complexes, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex, France.
Summary
This study investigates passive scalar advection in turbulent flows. Helical flow structures significantly enhance effective diffusivity, especially at low molecular diffusivity, a finding explained by a novel second-order approximation.
Area of Science:
- Fluid dynamics
- Turbulence theory
- Statistical mechanics
Background:
- Passive scalar advection is crucial in various physical phenomena.
- Understanding effective diffusivity in turbulent flows is a key challenge.
- Quenched incompressible velocity fields provide a simplified yet relevant model system.
Purpose of the Study:
- To investigate the advection of a passive scalar by a quenched incompressible velocity field.
- To analyze the role of helicity in modifying effective diffusivity.
- To develop and validate approximation schemes for predicting this behavior.
Main Methods:
- Extensive high-precision numerical simulations.
- Application of second-order self-consistent perturbation theory.
- Development and analysis of novel approximation schemes.
Main Results:
- Second-order perturbation theory accurately predicts effective diffusivity in non-helical fields.
- Helical flow fields exhibit a strong, nonperturbative enhancement of effective diffusivity.
- This enhancement is most pronounced for small bare molecular diffusivity.
Conclusions:
- Helicity in turbulent flows significantly enhances effective diffusivity through a second-order effect.
- The helical component amplifies the non-helical part, which then renormalizes molecular diffusivity.
- The findings are particularly relevant for systems with low bare molecular diffusivity.