Looking for a laminar-turbulent edge with Nektar++

Stanisław Gepner (Warsaw University of Technology)

For a limited number of flows, like the Taylor-Couette, tools of linear stability might provide explanation for the transition process as a sequence of consecutive supercritical bifurcations. In case of such flows, past the critical threshold, transition process manifests in the entire domain, homogeneously and happens in a relatively short time. Yet for a few canonical flows, like the plane Poiseuille flow, plane Couette flow or the pipe flow linear stability fails to predict transition altogether, since it happens far from any limits of stability or despite the absolute linear stability of the flow. In case of those, transition is sub-critical and results from finite amplitude disturbances that distort the laminar profile enough to trigger a prolonged nonlinear response of the system. Due to its sub-critical character precise parameter determination where nonlinear states can be sustained is difficult. Rather there seem to exist two limits, one below which the flow returns to its laminar form, and the other where fully turbulent state is sustained. In between the two limits, in the intermediate range, evolution of the flow seems to behave as a combination of coexisting laminar and turbulent states forming irregular and nonstationary flow patterns. Investigations of flows in the transitional regime focus on different aspects. On one hand interaction of large scale, turbulent laminar patterns, such as bands or puffs coexisting with laminar regions is investigated. On the other, interest is given to more local invariant solutions of the Navier-Stokes. Those are usually sought in constrained domains with related coherent structures, suggested to form building blocks of large-scale turbulence. In this work we focus on investigations of the flow dynamics in this intermediate regime of two types of flows, the zero-mean Couette-Poiseuille configuration and a square duct flow.