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Updated: Jun 28, 2026

The Diffusion of Passive Tracers in Laminar Shear Flow
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Localization and spectral phase transition in an open advecting-diffusing three-dimensional Stokes flow.

M Giona1, S Cerbelli

  • 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
PubMed
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.

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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.