UNSPECIFIED. (1999) Stability analysis of perturbed plane Couette flow. PHYSICS OF FLUIDS, 11 (5). pp. 1187-1195. ISSN 1070-6631

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. 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 Re-c = 230, beta(c) = 1.3 for rho = 0.086 and Re(c)approximate to 550, beta(c)approximate to 1.5 for rho = 0.043, where beta is the spanwise wave number and 2 rho is the 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 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. (C) 1999 American Institute of Physics. [S1070-6631(99)00305-0].

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