From patterns in turbulence to the buckling of shells – the role of unstable invariant solutions in nonlinear mechanics

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Date and time 06.05.2021 12:1513:15  
Online https://ethz.zoom.us/j/94817809233?pwd=N0pzbnQwSFFTQnVPcVR3SkNrd29OQT09
Speaker Prof. Tobias Schneider Emergent Complexity in Physical Systems Laboratory, EPFL Lausanne
Category Conferences - Seminars
Abstract: 
The transition to turbulence of fluid flows is ubiquitous, arising in our every-day experience when we ride a bicycle or take off in an airplane. Despite this ubiquity, the laminar-turbulent transition in wall-bounded flows is one of the least understood phenomena in fluid mechanics. During transition, the flow may self-organize into patterns with regular spatial and temporal structure, whose origins remain unexplained. A canonical flow exhibiting a large variety of complex spatio-temporal flow patterns is thermal convection in a fluid layer between two parallel plates kept at different temperature and inclined against gravity. We study the dynamics of the so-called inclined layer convection (ILC) system, using a fully nonlinear dynamical systems approach based on a state space analysis of the governing equations. Exploiting the computational power of our highly parallelized numerical continuation tools (www.channelflow.ch), we construct a large set of invariant solutions of ILC and discuss their bifurcation structure. We show that unstable equilibria, travelling waves, periodic orbits and heteroclinic orbits form dynamical networks that support moderately complex chaotic dynamics.
The introduced nonlinear dynamical systems methods centered around invariant solutions are not only revolutionizing our understanding of fluid turbulence but they may also help explain complex behaviour in other intrinsically nonlinear mechanical systems. We will specifically argue that unstable elastic equilibria control when thin-walled cylindrical shells such as rocket walls or soda cans buckle and collapse. This may open avenues towards predicting the notoriously imperfect-sensitive load-carrying capacity of shell structures without prior knowledge of the shell’s defects.

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