1999/05/01 by Dwight Barkley, Laurette S. Tuckerman · 2 citations
Earth and Planetary Sciences · Engineering · Physics and Astronomy · #Bifurcation #Classical mechanics #Couette flow #Flow (mathematics) #Fluid Dynamics and Turbulent Flows #Fluid Dynamics and Vibration Analysis #Geometry #Instability #Linear stability #Mechanics #Meteorological Phenomena and Simulations #Nonlinear system #Physics #Plane (geometry) #Ribbon #Taylor–Couette flow #Vortex #physics.flu-dyn
paper · pdf · doi:10.1063/1.869987
published as Physics of Fluids 11, 1187-1195 (1999)
openalex publication_date 1999/05/01 · arxiv created 2003/12/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.