New plane shear flows

Author: Conley, Andrew

Year: 1994

Degree: Dissertation (Ph.D.)

Advisor: Keller, Herbert Bishop

Committee Members: Keller, Herbert Bishop; Pullin, Dale Ian; Meiron, Daniel I.; Saffman, Philip G.

Option: Applied And Computational Mathematics

DOI: 10.7907/T34K-J848

Abstract

A classical problem in fluid dynamics is the study of the stability of plane Couette flow. This flow experimentally sustains turbulence for Reynolds numbers greater than 1440±40 (see [10],[5]). (The Reynolds number is based on channel width and wall velocity difference). Since plane Couette flow is linearly stable for all Reynolds numbers, obtaining non-trivial mathematical solutions to the plane Couette flow equations is difficult. However, M. Nagata [6] finds a non-trivial numerical solution of the plane Couette flow equations at low Reynolds number. We confirm these solutions. We compute the minimum Reynolds number at which they exist. We study their stability. We also study the effect of a Coriolis force on plane Poiseuille flow.

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