MEchanics GAthering -MEGA- Seminar: Spots and stripes: How turbulent-laminar patterns form in shear flows

When laminar shear flows undergo the transition to turbulence, patches of laminar and turbulent flow often coexist in space. These patches may form robust turbulent-laminar patterns. Prominent examples in wall-bounded shear flows are isolated turbulent spots and regular oblique stripes. Both examples have been observed in many experiments and simulations for more than 50 years, but how turbulent flow self-organizes such patterns is poorly understood. Here, we apply concepts of nonlinear dynamical systems theory to two types of shear flows, plane Couette flow and inclined convection, leading to a description of turbulent-laminar spots and stripes in terms of their exact invariant states. As exact solutions to the fully nonlinear governing equations, these invariant states are important reference states for studying the complex dynamics of turbulence. Exact invariant states representing spots and stripes arise in bifurcations of the systems that are associated to pattern forming instabilities and explain the origin of turbulent-laminar patterns in these shear flows.