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Breaking time reversal symmetry by viscous dephasing
Bruno Eckhardt1, Erwan Hascoët
1Fachbereich Physik, Philipps Universität Marburg, D-35032 Marburg, Germany.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 26, 2005
Summary
Periodic driving of Stokes flow typically breaks time-reversal symmetry, leading to chaotic advection. This occurs due to viscous dephasing in flow eigenmodes, even with reversible driving forces.
Area of Science:
- Fluid dynamics
- Nonlinear dynamics
- Rheology
Background:
- Stokes flow describes slow, viscous fluid motion.
- Time-reversal symmetry is a fundamental concept in physics.
- Chaotic advection can arise from time-dependent flows.
Purpose of the Study:
- To investigate the impact of reversible periodic driving on Stokes flow reversibility.
- To identify the mechanisms leading to broken time-reversal symmetry in driven flows.
- To demonstrate the preparation for chaotic advection.
Main Methods:
- Analysis of Stokes operator eigenmodes.
- Frequency and damping dependence of phase delays.
- Theoretical illustration using a 2D vortex pattern in a magnetic field-driven flow.
Main Results:
- Reversible periodic driving generally results in irreversible flow fields.
- Viscous dephasing of eigenmodes destroys time-reversal symmetry.
- The effect is frequency and damping dependent.
Conclusions:
- Periodic driving of Stokes flow inherently leads to irreversibility.
- This irreversibility is a precursor to chaotic advection.
- The findings are generalizable and illustrated by specific flow examples.