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Published on: April 4, 2016
On passage through resonances in volume-preserving systems
D L Vainchtein1, A I Neishtadt, I Mezic
1School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA.
Chaos (Woodbury, N.Y.)
|January 4, 2007
Summary
This study explores resonance phenomena in multiscale systems, revealing how multiple passages through resonance induce chaotic advection and mixing, which can be modeled by diffusion.
Area of Science:
- Multiscale Dynamics
- Fluid Mechanics
- Nonlinear Systems
Background:
- Resonance processes are prevalent in slow-fast multiscale systems.
- Understanding these phenomena is crucial for predicting system behavior.
Purpose of the Study:
- To develop a general theory for resonance capture and scattering in 3D volume-preserving multiscale systems.
- To apply this theory to kinematic models inspired by Taylor-Couette flows.
- To analyze the impact of resonance passages on chaotic advection and mixing.
Main Methods:
- Development of a general theory for resonance processes.
- Application to kinematic models of viscous Taylor-Couette flows.
- Analysis of single and multiple passages through resonance.
- Calculation of mixing domain width and mixing time.
- Modeling mixing using a diffusion equation.
Main Results:
- A general theory for resonance capture and scattering in 3D volume-preserving systems is proposed.
- Single resonance passages are described, while multiple passages lead to chaotic advection and mixing.
- The width of the mixing domain and characteristic mixing time are calculated.
- Resultant mixing is effectively described by a diffusion equation.
Conclusions:
- Resonance phenomena play a key role in mixing within multiscale systems.
- The study provides a theoretical framework and quantitative estimates for resonance-induced mixing.
- The findings have implications for understanding chaotic advection in fluid dynamics.
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