Mean field model for turbulence transition in plane Poiseuille flow

In the pipe flow model of Dwight Barkley the main idea is to model pipe flow as an excitable, bistable medium. Using a one-dimensional FitzHugh-Nagumo-type reaction-advection-diffusion system with two variables the model captures qualitatively a surprising number of features of the turbulence transition in pipe flow. Motivated by this success,...

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

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...

Direct and noisy transitions in a model shear flow

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 2D simplified model of the transition to...