Date of Award

Spring 2017

Project Type

Dissertation

Program or Major

Mathematics

Degree Name

Doctor of Philosophy

First Advisor

John F Gibson

Second Advisor

Gregory P Chini

Third Advisor

Mark E Lyon

Abstract

This thesis examines the existence and structure of spatially-localized, invariant solutions of plane Couette flow (PCF). This work serves to help expand a dynamical systems based perspective of the transition to turbulence in shear flows to include spatially-extended domains. Particular attention is paid to the relation of these invariant solutions to the turbulent-laminar banded patterns observed in PCF at transitional Reynolds numbers. Specific contributions include an analysis of the predominantly linear far-field structure or "tails" of localized solutions and the construction of a doubly-localized equilibrium solution -- the first doubly-localized invariant solution of a wall-bounded shear flow to be found.

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