An optimal path to transition in a duct
This paper is concerned with the transition of the laminar flow in a duct of square cross section. As in the similar case of pipe flow, the motion is linearly stable for all Reynolds numbers, rendering this flow a suitable candidate for a study of the 'bypass' path to turbulence. It has al...
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Published in | Philosophical transactions of the Royal Society of London. Series A: Mathematical, physical, and engineering sciences Vol. 367; no. 1888; pp. 529 - 544 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
London
The Royal Society
13.02.2009
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Subjects | |
Online Access | Get full text |
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Summary: | This paper is concerned with the transition of the laminar flow in a duct of square cross section. As in the similar case of pipe flow, the motion is linearly stable for all Reynolds numbers, rendering this flow a suitable candidate for a study of the 'bypass' path to turbulence. It has already been shown that the classical linear optimal perturbation problem, yielding optimal disturbances in the form of longitudinal vortices, fails to provide an 'optimal' path to turbulence, i.e. optimal perturbations do not elicit a significant nonlinear response from the flow. Previous simulations have also indicated that a pair of travelling waves generates immediately, by nonlinear quadratic interactions, an unstable mean flow distortion, responsible for rapid breakdown. By the use of functions quantifying the sensitivity of the motion to deviations in the base flow, the optimal travelling wave associated with its specific defect is found by a variational approach. This optimal solution is then integrated in time and shown to display a qualitative similarity to the so-called 'minimal defect', for the same parameters. Finally, numerical simulations of an 'edge state' are conducted, to identify an unstable solution that mediates laminar-turbulent transition and relate it to results of the optimization procedure. |
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Bibliography: | istex:2E91B9211075834AF8D9E60771DBBD72CF8F69DB href:529.pdf Present address: LEA, SP2MI Téléport 2, Bd Marie et Pierre Curie, BP 30179, 89962 Futuroscope Chasseneuil Cedex, France. ArticleID:rsta20080191 ark:/67375/V84-RK1D5N80-3 Theme Issue 'Turbulence transition in pipe flow: 125th anniversary of the publication of Reynolds' paper' compiled by Bruno Eckhardt ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 |
ISSN: | 1364-503X 1471-2962 |
DOI: | 10.1098/rsta.2008.0191 |