Instability in pipe flow
- 15 January 2008
- journal article
- Published by Proceedings of the National Academy of Sciences in Proceedings of the National Academy of Sciences of the United States of America
- Vol. 105 (2), 428-430
- https://doi.org/10.1073/pnas.0709172104
Abstract
The long-puzzling, unphysical result that linear stability analyses lead to no transition in pipe flow, even at infinite Reynolds number, is ascribed to the use of stick boundary conditions, because they ignore the amplitude variations associated with the roughness of the wall. Once that length scale is introduced (here, crudely, through a corrugated pipe), linear stability analyses lead to stable vortex formation at low Reynolds number above a finite amplitude of the corrugation and unsteady flow at a higher Reynolds number, where indications are that the vortex dislodges. Remarkably, extrapolation to infinite Reynolds number of both of these transitions leads to a finite and nearly identical value of the amplitude, implying that below this amplitude, the vortex cannot form because the wall is too smooth and, hence, stick boundary results prevail.This publication has 25 references indexed in Scilit:
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