Characterization of the hairpin vortex solution in plane Couette flow

Sotos C. Generalis; Tomoaki Itano

doi:10.1103/PhysRevE.82.066308

Characterization of the hairpin vortex solution in plane Couette flow

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Abstract

Quantitative evidence that establishes the existence of the hairpin vortex state (HVS) in plane Couette flow (PCF) is provided in this work. The evidence presented in this paper shows that the HVS can be obtained via homotopy from a flow with a simple geometrical configuration, namely, the laterally heated flow (LHF). Although the early stages of bifurcations of LHF have been previously investigated, our linear stability analysis reveals that the root in the LHF yields multiple branches via symmetry breaking. These branches connect to the PCF manifold as steady nonlinear amplitude solutions. Moreover, we show that the HVS has a direct bifurcation route to the Rayleigh-Bénard convection. © 2010 The American Physical Society.

Original language	English
Article number	066308
Number of pages	7
Journal	Physical Review E
Volume	82
Issue number	6
DOIs	https://doi.org/10.1103/PhysRevE.82.066308
Publication status	Published - 10 Dec 2010

Bibliographical note

Copyright 2010 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Generalis, Sotos C and Itano, Tomoaki (2010). Characterization of the hairpin vortex solution in plane Couette flow.<http://eprints.aston.ac.uk/10922/> Physical Review E, 82 (6), 066308 and may be found at http://dx.doi.org/10.1103/PhysRevE.82.066308

Keywords

hairpin vortex state
plane Couette flow
laterally heated flow
bifurcations
Rayleigh-Bénard convection

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10.1103/PhysRevE.82.066308

Characterization of the hairpin vortex solution in plane Couette flow
Copyright 2010 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Generalis, Sotos C and Itano, Tomoaki (2010). Characterization of the hairpin vortex solution in plane Couette flow.<http://eprints.aston.ac.uk/10922/> Physical Review E, 82 (6), 066308 and may be found at http://dx.doi.org/10.1103/PhysRevE.82.066308

http://link.aps.org/doi/10.1103/PhysRevE.82.066308

Cite this

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title = "Characterization of the hairpin vortex solution in plane Couette flow",

abstract = "Quantitative evidence that establishes the existence of the hairpin vortex state (HVS) in plane Couette flow (PCF) is provided in this work. The evidence presented in this paper shows that the HVS can be obtained via homotopy from a flow with a simple geometrical configuration, namely, the laterally heated flow (LHF). Although the early stages of bifurcations of LHF have been previously investigated, our linear stability analysis reveals that the root in the LHF yields multiple branches via symmetry breaking. These branches connect to the PCF manifold as steady nonlinear amplitude solutions. Moreover, we show that the HVS has a direct bifurcation route to the Rayleigh-B{\'e}nard convection. {\textcopyright} 2010 The American Physical Society.",

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AB - Quantitative evidence that establishes the existence of the hairpin vortex state (HVS) in plane Couette flow (PCF) is provided in this work. The evidence presented in this paper shows that the HVS can be obtained via homotopy from a flow with a simple geometrical configuration, namely, the laterally heated flow (LHF). Although the early stages of bifurcations of LHF have been previously investigated, our linear stability analysis reveals that the root in the LHF yields multiple branches via symmetry breaking. These branches connect to the PCF manifold as steady nonlinear amplitude solutions. Moreover, we show that the HVS has a direct bifurcation route to the Rayleigh-Bénard convection. © 2010 The American Physical Society.

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Characterization of the hairpin vortex solution in plane Couette flow

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Keywords

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