  Transition to turbulence dramatically alters the properties of fluid flows.
In most canonical shear flows, the laminar flow is linearly stable and a
finite-amplitude perturbation is necessary to trigger transition. Controlling
transition to turbulence is achieved via the broadening or narrowing of the
basin of attraction of the laminar flow. In this paper, a novel methodology to
assess the robustness of the laminar flow and the efficiency of control
strategies is introduced. It relies on the statistical sampling of the phase
space neighborhood around the laminar flow in order to assess the transition
probability of perturbations as a function of their energy. This approach is
applied to a canonical flow (plane Couette flow) and provides invaluable
insight: in the presence of the chosen control, transition is significantly
suppressed whereas plausible scalar indicators of the nonlinear stability of
the flow, such as the edge state energy, do not provide conclusive predictions.
The methodology presented here in the context of transition to turbulence is
applicable to any nonlinear system displaying finite-amplitude instability.
