Turbulence Transition in Shear Flows and Dynamical Systems Theory

Turbulence is allegedly “the most important unsolved problem of classical physics” (attributed to Richard Feynman). While the equations of motion are known since almost 150 years and despite the work of many physicists, in particular the transition to turbulence in linearly stable shear flows eva...

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Bibliographic Details
Main Author: Kreilos, Tobias
Contributors: Eckhardt, Bruno (Prof. Dr.) (Thesis advisor)
Format: Dissertation
Language:English
Published: Philipps-Universität Marburg 2014
Physik
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Summary:Turbulence is allegedly “the most important unsolved problem of classical physics” (attributed to Richard Feynman). While the equations of motion are known since almost 150 years and despite the work of many physicists, in particular the transition to turbulence in linearly stable shear flows evades a satisfying description. In recent decades, the availability of more powerful computers and developments in chaos theory have provided the basis for considerable progress in our understanding of this issue. The successful work of many scientists proved dynamical systems theory to be a useful and important tool to analyze transitional turbulence in fluid mechanics, allowing to explain observed phenomena such as transition thresholds and transient lifetimes through bifurcation analyses and the identification of underlying state space structures. In this thesis we continue on that path with direct numerical simulations in plane Couette flow, the asymptotic suction boundary layer and Blasius boundary layers. We explore the state space structures and bifurcations in plane Couette flow, study the threshold dynamics in the ASBL and develop a model for the spatio-temporal dynamics in the boundary layers. The results show how the insights obtained for parallel, bounded shear flows can be transferred to spatially developing external flows.
DOI:https://doi.org/10.17192/z2014.0356