When a finite amplitude perturbation triggers turbulence in a linearly stable shear flow, spatio-temporal patterns emerge in the chaotically fluctuating flow. Those patterns appear to be captured by dynamically unstable spatially localized exact invariant solutions of the nonlinear 3D Navier-Stokes equations. Specific equilibrium and traveling wave solutions are organized in a snakes-and-ladders structure strikingly similar to that observed in simpler pattern-forming PDE systems, suggesting that well-developed theories of patterns in simpler PDE models carry over to transitional turbulent flows. We characterize localized solutions of plane Couette flow, demonstrate how those states emerge from Wavy-Vortex flow in the Taylor-Couette system and discuss how they are related to laminar-turbulent stripe patterns commonly observed in the flow dynamics.
Additionally, we will discuss how the dynamical systems concepts based on fully nonlinear invariant solutions which are advancing our understanding of transitional shear flows can be carried over to other problems in nonlinear mechanics such as the buckling and collapse of thin elastic shells.
Bio: Tobias Schneider is an assistant professor in the School of Engineering at EPFL, the Swiss Federal Institute of Technology Lausanne. He received his doctoral degree in 2007 from the University of Marburg in Germany working on the transition to turbulence in pipe flow under the supervision of Prof. Bruno Eckhardt. He then joined Harvard University as a postdoctoral fellow working primarily with Prof. Michael P. Brenner. In 2012 Tobias Schneider returned to Europe to establish an independent research group at the Max-Planck Institute for Dynamics and Self-Organization in Goettingen. Since 2014, he is working at EPFL, where he teaches fluid mechanics and heads the 'Emergent Complexity in Physical Systems' laboratory.