Abstract

Transition to turbulence is a common instability in which a laminar flow evolves into spatio-temporal chaos. It affects a number of applications involving the displacement of fluid such as fluid transport and aerodynamics. When a flow transitions to turbulence, wall friction and drag increase, impacting negatively the above applications and creating the need for control. The engineering literature has, so far, mainly focused on alleviating the effects of turbulence. We take a different approach: we do not consider fully developed turbulent flows but rather aim to postpone the transition to it.

In this talk, we will consider one of the simplest examples of transitional flows (plane Couette flow), where transition occurs through a finite-amplitude instability: a perturbation of sufficient energy is necessary to trigger transition. We will discuss two ideas to facilitate the control of transition. Firstly, we will assess the robustness of the laminar flow by computing the probability that random perturbations transition as a function of their amplitude. Secondly, as transition involves spatially localized turbulent spots, we will discuss the dynamics of steady spatially localized solutions and determine under which conditions they yield long-lasting chaos. Both of these ideas will be presented in the absence of control to establish a benchmark and will then be tested in the presence of a well-studied control strategy. Quantitative conclusions on the efficiency of the control will be drawn.