  The transition to turbulence in flows where the laminar profile is linearly
stable requires perturbations of finite amplitude. "Optimal" perturbations are
distinguished as extrema of certain functionals, and different functionals give
different optima. We here discuss the phase space structure of a 2-d simplified
model of the transition to turbulence and discuss optimal perturbations with
respect to three criteria: energy of the initial condition, energy dissipation
of the initial condition and amplitude of noise in a stochastic transition. We
find that the states that trigger the transition are different in the three
cases, but show the same scaling with Reynolds number.
