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Transition to turbulence in duct flow

Published online by Cambridge University Press:  17 January 2008

DAMIEN BIAU ,
HOUSSAM SOUEID  and
ALESSANDRO BOTTARO
DAMIEN BIAU
Affiliation:
Università di Genova, DICAT, Via Montallegro 1, 16145 Genova, Italy
HOUSSAM SOUEID
Affiliation:
Università di Genova, DICAT, Via Montallegro 1, 16145 Genova, Italy
ALESSANDRO BOTTARO
Affiliation:
Università di Genova, DICAT, Via Montallegro 1, 16145 Genova, Italy
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Abstract

The transition of the flow in a duct of square cross-section is studied. Like in the similar case of the pipe flow, the motion is linearly stable for all Reynolds numbers; this flow is thus a good candidate to investigate the ‘bypass’ path to turbulence. Initially the so-called ‘linear optimal perturbation problem’ is formulated and solved, yielding optimal disturbances in the form of longitudinal vortices. Such optimals, however, fail to elicit a significant response from the system in the nonlinear regime. Thus, streamwise-inhomogeneous sub-optimal disturbances are focused upon; nonlinear quadratic interactions are immediately caused by such initial perturbations and an unstable streamwise-homogeneous large-amplitude mode rapidly emerges. The subsequent evolution of the flow, at a value of the Reynolds number at the boundary between fully developed turbulence and relaminarization, shows the alternance of patterns with two pairs of large-scale vortices near opposing parallel walls. Such edge states bear a resemblance to optimal disturbances.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 596 , 25 January 2008 , pp. 133 - 142
Copyright
Copyright © Cambridge University Press 2008

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