Title:
Charting the State Space of Plane Couette Flow: Equilibria, Relative Equilibria, and Heteroclinic Connections
Charting the State Space of Plane Couette Flow: Equilibria, Relative Equilibria, and Heteroclinic Connections
Author(s)
Halcrow, Jonathan
Advisor(s)
Cvitanović, Predrag
Editor(s)
Collections
Supplementary to
Permanent Link
Abstract
The study of turbulence has been dominated historically by a bottom-up approach,
with a much stronger emphasis on the physical structure of flows than on that of the dynam-
ical state space. Turbulence has traditionally been described in terms of various visually
recognizable physical features, such as waves and vortices. Thanks to recent theoretical as
well as experimental advancements, it is now possible to take a more top-down approach
to turbulence. Recent work has uncovered non-trivial equilibria as well as relative periodic
orbits in several turbulent systems. Furthermore, it is now possible to verify theoretical
results at a high degree of precision, thanks to an experimental technique known as Particle
Image Velocimetry. These results squarely frame moderate Reynolds number Re turbulence
in boundary shear flows as a tractable dynamical systems problem.
In this thesis, I intend to elucidate the finer structure of the state space of moderate Re
wall-bounded turbulent flows in hope of providing a more accurate and precise description of
this complex phenomenon. Computation of new undiscovered equilibria, relative equilibria,
and their heteroclinic connections provide a skeleton upon which a numerically accurate
description of turbulence can be framed. The behavior of the equilibria under variation of
Reynolds number and cell aspect ratios is also examined. It is hoped that this description
of the state space will provide new avenues for research into nonlinear control systems for
shear flows as well as quantitative predictions of transport properties of moderate Re fluid
flows.
Sponsor
Date Issued
2008-07-08
Extent
Resource Type
Text
Resource Subtype
Dissertation