Finite Amplitude Waves in Plane Poiseuille Flow

Author: Pugh, Jeffrey David

Year: 1988

Degree: Dissertation (Ph.D.)

Advisor: Saffman, Philip G.

Committee Members: Saffman, Philip G.; Meiron, Daniel I.; Kubota, Toshi; Lorenz, Jens; Leonard, Anthony

Option: Aeronautics

DOI: 10.7907/XHFQ-MJ23

Abstract

Nonlinear behavior in plane Poiseuille flow has attracted theoretical interest over the last decade, both because of its tractability and because it is believed that some of the results may be applicable to phenomena occurring in the boundary layer. We have investigated the existence of three-dimensional finite amplitude waves in plane Poiseuille flow, in the hope of finding candidates for a class of simple flows which might provide insight into the nature of turbulence. These so-called vortical states would exist as attractors for the turbulent flow and mimic many of its properties.

One of the requisite properties of these simple flows is existence at the low Reynolds numbers observed in experimental studies of transition to turbulence in plane Poiseuille flow. Although no such three-dimensional solutions were found in our study, a number of new insights have been made into the structure and stability of two- and three-dimensional steady wave solutions in plane Poiseuille flow. These in turn suggest new areas of investigation for finding vortical states.

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