Abstract
The homoclinic orbit from/to the unstable periodic orbit found by Kawahara and Kida (2001) in minimal plane Couette flow is numerically computed by use of direct numerical simulation and multiple shooting method which allow us to perform the long-time integration of the Navier-Stokes equation. This homoclinic orbit yields the infinite number of transversal intersections between the unstable and stable manifolds of the periodic orbit in a Poincare section, leading to chaotic dynamics described mathematically by Smale's horseshoe map. Along the homoclinic orbit vortical structures and the associated energy dissipation are observed to be highly localized on the crest or valley of a velocity streak, in contrast to the familiar near-wall regeneration cycle.
