Laminarization of minimal plane Couette flow: Going beyond the basin of attraction of turbulence

Abstract

Laminarization of minimal plane Couette turbulence is achieved numerically through short-time imposition of weak spanwise system rotation. A laminarization strategy presented in this Letter is inspired by investigation of the phase-space structure in the vicinity of a recently found unstable periodic orbit [G. Kawahara and S. Kida, “Periodic motion embedded in plane Couette turbulence: regeneration cycle and burst,” J. Fluid Mech. 449, 291 (2001)]. The periodic orbit, which a turbulent state occasionally approaches, and its local stable manifold are found to form the separatrix between the basin of attraction of turbulent and laminar flows. The introduction of the slight rotation during its approach to the periodic orbit enables the state to go beyond the basin of attraction of the turbulence toward the laminar flow. The global stabilization of the unstable periodic orbit by the method of controlling chaos is also performed to accomplish the laminarization without waiting until the natural approach.