The Rayleigh Problem for the Interior of a Torus

[+] Author and Article Information
W. J. Rae, C. J. Ollila

Department of Mechanical and Aerospace Engineering, State University of New York at Buffalo, Buffalo, NY 14260

J. Fluids Eng 115(4), 603-607 (Dec 01, 1993) (5 pages) doi:10.1115/1.2910186 History: Received April 03, 1993; Revised September 13, 1993; Online May 23, 2008


This paper contains a description of the low Reynolds number flow inside a torus which has been set impulsively in motion about its central axis. The moving wall drags with it a primary flow confined to a sheath that grows steadily toward the center of the torus cross section. The primary flow in turn produces centrifugal and Coriolis accelerations which lead to secondary flows in the cross-sectional plane. At very long time the secondary flows subside, and the primary flow approaches a condition of solid-body rotation. The present analysis treats this problem in the thin-torus limit, where the cross-sectional radius is small compared to the toroidal radius, and is restricted to wall velocities small enough to support a low Reynolds-number assumption. At this level of approximation, the flow is characterized by a single dimensionless parameter, analogous to the Dean number.

Copyright © 1993 by The American Society of Mechanical Engineers
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