LAUSR

The onset of transient turbulence in minimal plane Couette flow has been identified theoretically as homoclinic tangency with respect to a simple edge state for the Navier–Stokes equation, i.e., the gentle periodic orbit (the lower branch of a saddle-node pair) found by Kawahara & Kida (J. Fluid Mech., vol. 449, 2001, pp. 291–300). The first tangency of a pair of distinct homoclinic orbits to this periodic edge state has been discovered at Reynolds number $Re\equiv Uh/\unicode[STIX]{x1D708}=Re_{T}\approx 240.88$ ( $U$ , $h$ , and $\unicode[STIX]{x1D708}$ being half the difference of the two wall velocities, half the wall separation, and the kinematic viscosity of fluid, respectively). At $Re>Re_{T}$ a Smale horseshoe appears on the Poincaré section through transversal homoclinic points to generate a transient chaos that eventually relaminarises. In numerical experiments a sustaining chaos, which is a consequence of period-doubling cascade stemming from the upper branch of another saddle-node pair of periodic orbits, is observed in a narrow range of the Reynolds number, $Re\approx 240.40$ –240.46. At the upper edge of this $Re$ range it is found that the chaotic set touches the lower branch of this pair, i.e., another edge state. The corresponding chaotic attractor is replaced by a chaotic saddle at $Re\approx 240.46$ , and subsequently this saddle touches the gentle periodic edge state on the boundary of the laminar basin at the tangency Reynolds number $Re=Re_{T}$ . After this crisis on the boundary of the laminar basin, for $Re>Re_{T}$ , chaotic transients that eventually relaminarise can be observed.