Dynamic feedback control of edge states in plane Poiseuille flow

The transition to turbulence in many wall-bounded parallel shear flows, such as pipe or plane Poiseuille flow, is connected to the presence of a lower-dimensional manifold in state space, the edge of chaos, which distinguishes between initial conditions resulting in laminar or turbulent flow. States on the edge manifold have thus at least one unstable direction, and the dynamics will not remain confined to it. However, feedback stabilisation method can be used to remove the effect of the unstable direction, as demonstrated for pipe flow by Willis et al JFM 2017. Here, we focus on similar strategies in plane Poiseuille flow. We investigate the effect of a dynamic pressure-based feedback control on the stable and unstable directions in order to stabilise states on the edge.