Session Cc - General Instabilities.
ORAL session, Sunday, November 23
303, Moscone Center
Motivated by recent experiments by Bottin et al.(S. Bottin, O. Dauchot, and F. Daviaud, submitted to J. Fluid Mech.), we have performed a computational linear and nonlinear stability analysis of plane Couette flow perturbed by a small ribbon at mid-gap. The ribbon is infinitesimal in the streamwise direction, has height approximately one-tenth of the cross-channel dimension, and is infinite in the spanwise direction. The 2D steady flow in this geometry differs from plane Couette flow by the presence of a small counter-rotating region immediately surrounding the ribbon, as in the finite amplitude solutions to plane Couette flow computed by Cherhabili and Ehrenstein(A. Cherhabili and U. Ehrenstein, Eur. J. Mech. B/Fluids 14), 677 (1995). and Coughlin(K. Coughlin, submitted to J. Fluid Mech.). This 2D steady flow is, unlike unperturbed plane Couette flow, linearly unstable at Re \approx 230 to a three-dimensional perturbation whose spanwise wavelength \lambda = 4.8 h agrees with that observed experimentally. Nonlinear stability computations show that bifurcation is subcritical. Full three-dimensional simulations evolve towards a flow containing streamwise vortices, as seen experimentally.