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Physics of Fluids / Volume 24 / Issue 1 / ARTICLES / Instability and Transition

Phys. Fluids 24, 014106 (2012); http://dx.doi.org/10.1063/1.3675899 (10 pages)

The linear stability of oscillating pipe flow

C. Thomas1, A. P. Bassom1, and P. J. Blennerhassett2

1School of Mathematics and Statistics, The University of Western Australia, Crawley, WA 6009, Australia
2School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia

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(Received 4 May 2011; accepted 2 December 2011; published online 11 January 2012)

An investigation is made of the three-dimensional linear stability of the Stokes layer generated within a fluid contained inside a long oscillating cylinder. Both longitudinal and torsional vibrations are examined and the system of disturbance equations derived using Floquet theory are solved using pseudospectral methods. Critical parameters for instability are obtained for an extensive range of pipe radii and longitudinal and azimuthal wavenumbers. For sufficiently small pipe diameters, three-dimensional perturbations are sometimes found to be more unstable than their two-dimensional counterparts. In contrast, at larger radii, the three-dimensional disturbance modes are less important and the two-dimensional versions are expected to be observed in practice. These results imply constraints on experiments that are designed to exhibit shear modes in oscillatory flow.

© 2012 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. FORMULATION
    1. Numerical methods
  3. RESULTS
    1. Longitudinal flow
    2. Torsional flow
  4. DISCUSSION

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KEYWORDS and PACS

Keywords

flow instability, fluid oscillations, pipe flow, shear flow, vibrations

PACS

  • 47.20.Ft

    Instability of shear flows (e.g., Kelvin-Helmholtz)

  • 47.60.Dx

    Flows in ducts and channels

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3675899

PUBLICATION DATA

ISSN

1070-6631 (print)  
1089-7666 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

For access to fully linked references, you need to log in.
    R. Verzicco and G. Vittori, “Direct simulation of transition in Stokes boundary layers,” Phys. Fluids 8, 1341 (1996)PHFLE6000008000006001341000001.

    J. Luo and X. Wu, “On the linear stability of a finite Stokes layer: instantaneous versus Floquet modes,” Phys. Fluids 22, 054106 (2010)PHFLE6000022000005054106000001.


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