Spatially-Localized Solutions of Plane Couette Flow

Evan Wells Brand, University of New Hampshire, Durham

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.