Unstable manifolds computation for the 2-D plane Poiseuille flow

Abstract

We follow the unstable manifold of periodic and quasi-periodic solutions for the Poiseuille problem, using two formulations: holding constant flux or mean pressure gradient. By means of a numerical integrator of the Navier-Stokes equations, we let the fluid evolve from a perturbed unstable solution. We detect several connections among different configurations of the flow such as laminar, periodic, quasi-periodic with 2 or 3 basic frequencies and more complex sets that we have not been able to classify.