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Time-dependent helical waves in rotating pipe flow

Published online by Cambridge University Press:  26 April 2006

Michael J. Landman
Michael J. Landman
Affiliation:
Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012 USA Present address: BHP Melbourne Research Laboratories, PO Box 264, Clayton, Vic 3168, Australia
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Abstract

The Navier-Stokes equations for flow in a rotating circular pipe are solved numerically, subject to imposing helical symmetry on the velocity field v = v(r, θ + αz,t). The helical symmetry is exploited by writing the equations of motion in helical variables, reducing the problem to two dimensions. A limited study of the pipe flow is made in the parameter space of the wavenumber α, and the axial and azimuthal Reynolds numbers. The steadily rotating waves previously studied by Toplosky & Akylas (1988), which arise from the linear instability of the basic steady flow, are found to undergo a series of bifurcations, through periodic to aperiodic time dependence. The relevance of these results to the mechanism of laminar-turbulent transition in a stationary pipe is discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 221 , December 1990 , pp. 289 - 310
Copyright
© 1990 Cambridge University Press

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