dorsal/arxiv
View SchemaStability analysis of perturbed plane Couette flow
| Authors | Dwight Barkley, Laurette S. Tuckerman |
|---|---|
| Categories | |
| ArXiv ID | physics/0312048 |
| URL | https://arxiv.org/abs/physics/0312048 |
| DOI | 10.1063/1.869987 |
| Journal | Physics of Fluids 11, 1187-1195 (1999) |
Abstract
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. 2D 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 2D steady flow loses stability to 3D eigenmodes at Re = 230, beta = 1.3 for rho = 0.086 and Re = 550, beta = 1.5 for rho = 0.043, where Re is the Reynolds number, beta is the spanwise wavenumber and rho is the half-height of the ribbon. For rho = 0.086, the bifurcation is determined to be subcritical by calculating the cubic term in the normal form equation from the timeseries of a single nonlinear simulation; steady 3D flows are found for Re as low as 200. The critical eigenmode and nonlinear 3D states contain streamwise vortices localized near the ribbon, whose streamwise extent increases with Re. All of these results agree well with experimental observations.
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"abstract": "Plane Couette flow perturbed by a spanwise oriented ribbon, similar to a\nconfiguration investigated experimentally at the Centre d\u0027Etudes de Saclay, is\ninvestigated numerically using a spectral-element code. 2D steady states are\ncomputed for the perturbed configuration; these differ from the unperturbed\nflows mainly by a region of counter-circulation surrounding the ribbon. The 2D\nsteady flow loses stability to 3D eigenmodes at Re = 230, beta = 1.3 for rho =\n0.086 and Re = 550, beta = 1.5 for rho = 0.043, where Re is the Reynolds\nnumber, beta is the spanwise wavenumber and rho is the half-height of the\nribbon. For rho = 0.086, the bifurcation is determined to be subcritical by\ncalculating the cubic term in the normal form equation from the timeseries of a\nsingle nonlinear simulation; steady 3D flows are found for Re as low as 200.\nThe critical eigenmode and nonlinear 3D states contain streamwise vortices\nlocalized near the ribbon, whose streamwise extent increases with Re. All of\nthese results agree well with experimental observations.",
"arxiv_id": "physics/0312048",
"authors": [
"Dwight Barkley",
"Laurette S. Tuckerman"
],
"categories": [
"physics.flu-dyn"
],
"doi": "10.1063/1.869987",
"journal_ref": "Physics of Fluids 11, 1187-1195 (1999)",
"title": "Stability analysis of perturbed plane Couette flow",
"url": "https://arxiv.org/abs/physics/0312048"
},
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