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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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| Format: | Dissertation |
| Sprache: | Englisch |
| Veröffentlicht: |
Philipps-Universität Marburg
2014
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| Online Zugang: | PDF-Volltext |
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| Zusammenfassung: | 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. |
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| DOI: | 10.17192/z2014.0356 |