Phys. Rev. Lett. 98, 204501 (2007) [4 pages]

Lower Branch Coherent States in Shear Flows: Transition and Control

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Jue Wang^1,*, John Gibson^2,†, and Fabian Waleffe^1,3,‡
¹Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706, USA
²Center for Nonlinear Sciences, School of Physics, Georgia Tech, Atlanta, Georgia 30332, USA
³Department of Engineering Physics, University of Wisconsin, Madison, Wisconsin 53706, USA

Received 6 March 2007; published 15 May 2007

Lower branch coherent states in plane Couette flow have an asymptotic structure that consists of O(1) streaks, O(R^-1) streamwise rolls and a weak sinusoidal wave that develops a critical layer, for large Reynolds number R. Higher harmonics become negligible. These unstable lower branch states appear to have a single unstable eigenvalue at all Reynolds numbers. These results suggest that lower branch coherent states control transition to turbulence and that they may be promising targets for new turbulence prevention strategies.

URL:

http://link.aps.org/doi/10.1103/PhysRevLett.98.204501

DOI:

10.1103/PhysRevLett.98.204501

PACS:

47.27.Cn, 47.27.De, 47.27.ed

^*Electronic address: wang@math.wisc.edu

^†Electronic address: gibson@cns.physics.gatech.edu

^‡Electronic address: waleffe@math.wisc.edu

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Phys. Rev. Lett. 98, 204501 (2007) [4 pages]

Lower Branch Coherent States in Shear Flows: Transition and Control