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Lower branch coherent states in shear flows: transition and control
Jue Wang1, John Gibson, Fabian Waleffe
1Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706, USA. wang@math.wisc.edu
Physical Review Letters
|August 7, 2007
Summary
Lower branch coherent states in plane Couette flow exhibit a specific structure and possess a single unstable eigenvalue, suggesting their crucial role in turbulence transition and potential for prevention strategies.
Area of Science:
- Fluid Dynamics
- Turbulence
- Nonlinear Dynamics
Background:
- Plane Couette flow is a fundamental model in fluid dynamics.
- Understanding the transition to turbulence is a key challenge.
- Coherent structures play a significant role in turbulent flows.
Purpose of the Study:
- To analyze the asymptotic structure of lower branch coherent states in plane Couette flow.
- To investigate the stability properties of these states.
- To explore the implications for turbulence control and prevention.
Main Methods:
- Asymptotic analysis for large Reynolds numbers (R).
- Examination of the structure involving streaks, streamwise rolls, and sinusoidal waves.
- Analysis of eigenvalues to determine stability.
Main Results:
- Identified an asymptotic structure of O(1) streaks, O(R(-1)) streamwise rolls, and a critical layer-forming sinusoidal wave.
- Found that higher harmonics are negligible.
- Observed a single unstable eigenvalue for these states across all Reynolds numbers.
Conclusions:
- Lower branch coherent states are unstable and appear to control transition to turbulence.
- These states represent promising targets for developing novel turbulence prevention strategies.
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