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Physics of Fluids / Volume 11 / Issue 5 / ARTICLES

Phys. Fluids 11, 1187 (1999); doi:10.1063/1.869987 (9 pages)

Stability analysis of perturbed plane Couette flow

Dwight Barkley1 and Laurette S. Tuckerman2

1Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom
2LIMSI-CNRS, BP 133, 91403 Orsay Cedex, France

(Received 16 December 1997; accepted 5 January 1999)

Plane Couette flow perturbed by a spanwise oriented ribbon, similar to a configuration investigated experimentally at the Centre d’Etudes de Saclay, is investigated numerically using a spectral-element code. Two-dimensional (2-D) steady states are computed for the perturbed configuration; these differ from the unperturbed flows mainly by a region of counter-circulation surrounding the ribbon. The 2-D steady flow loses stability to three-dimensional (3-D) eigenmodes at Rec = 230, βc = 1.3 for ρ = 0.086 and Rec ≈ 550, βc ≈ 1.5 for ρ = 0.043, where β is the spanwise wave number and 2ρ is the height of the ribbon. For ρ = 0.086, the bifurcation is determined to be subcritical by calculating the cubic term in the normal form equation from the time series of a single nonlinear simulation; steady 3-D flows are found for Re as low as 200. The critical eigenmode and nonlinear 3-D states contain streamwise vortices localized near the ribbon, whose streamwise extent increases with Re. All of these results agree well with experimental observations. © 1999 American Institute of Physics.

© 1999 American Institute of Physics

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KEYWORDS and PACS

Keywords

Couette flow, bifurcation, vortices, flow simulation, flow instability

PACS

ARTICLE DATA

Permalink
http://link.aip.org/link/doi/10.1063/1.869987

PUBLICATION DATA

ISSN:

1070-6631 (print)  
1089-7666 (online)

Publisher:

$abstract.society.value is a Member of CrossRef American Institute of Physics

For access to fully linked references, you need to log in.
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