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Updated: Jun 28, 2026
08:01
The Diffusion of Passive Tracers in Laminar Shear Flow
Published on: May 1, 2018
Localization and spectral phase transition in an open advecting-diffusing three-dimensional Stokes flow.
1Dipartimento di Ingegneria Chimica, Università di Roma La Sapienza, via Eudossiana 18, 00184 Roma, Italy. max@giona.ing.uniroma1.it
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 13, 2008
Summary
A phase transition in advection-diffusion flow between rotating cylinders is observed. Cylinder velocity variations control spectral properties, with a continuous order parameter and a discontinuous eigenvalue exponent at the critical point.
Area of Science:
- Fluid Dynamics
- Mathematical Physics
Background:
- Advection-diffusion phenomena are crucial in various scientific fields.
- Understanding steady-state characteristics in complex geometries is essential.
- Coaxial rotating cylinders present a unique system for studying fluid behavior.
Purpose of the Study:
- To characterize the steady-state behavior of a three-dimensional advecting-diffusing flow.
- To investigate phase transitions induced by independent cylinder rotation.
- To analyze the spectral properties of the advection-diffusion equation in this system.
Main Methods:
- Numerical simulation of a three-dimensional advecting-diffusing flow.
- Analysis of the dominant eigenvalue and eigenfunction.
- Investigation of spectral properties at high Péclet numbers.
Main Results:
- A phase transition occurs with varying cylinder velocities.
- The localization abscissa of the dominant eigenfunction acts as a continuous order parameter.
- The scaling exponent of the dominant eigenvalue's real part shows discontinuous behavior at the critical point.
Conclusions:
- Theoretical arguments support the observed numerical localization properties.
- The study provides a simplified explanation for the phase transition phenomenon.
- The findings offer insights into controlling spectral properties via cylinder velocity.
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