Direct versus noise-induced optimal transitions for a model shear flow

Abstract

The transition from laminar to turbulent flow in parallel shear flows like pipe flow or plane Couette flow is not due to a linear instability of the laminar profile but requires finite amplitude perturbations. The perturbations have to be strong enough that they cross the boundary to the basin of attraction of the turbulent regime. We use a 2-dimensional model of the transition to turbulence to explore the underlying phase space structure for optimal perturbations with respect to three different criteria: the energy of the initial condition, the energy dissipation of the initial condition and the amplitude of noise in a noise-induced transition. We find that the optimal transition states are different, but that the scaling with Reynolds number is the same in all three cases. Implications for full simulations will be discussed.