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Linear stability of rotating Hagen-Poiseuille flow

Published online by Cambridge University Press:  20 April 2006

Fredrick W. Cotton  and
Harold Salwen
Fredrick W. Cotton
Affiliation:
Department of Physics and Engineering Physics, Stevens Institute of Technology, Hoboken, N.J. 07030
Harold Salwen
Affiliation:
Department of Physics and Engineering Physics, Stevens Institute of Technology, Hoboken, N.J. 07030
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Abstract

Linear stability of rotating Hagen-Poiseuille flow has been investigated by an orthonormal expansion technique, confirming results by Pedley and Mackrodt and extending those results to higher values of the wavenumber |α|, the Reynolds number R, and the azimuthal index n. For |α| [gsim ] 2, the unstable region is pushed to considerably higher values of R and the angular velocity, Ω. In this region, the neutral stability curves obey a simple scaling, consistent with the unstable modes being centre modes. For n = 1, individual neutral stability curves have been calculated for several of the low-lying eigenmodes, revealing a complicated coupling between modes which manifests itself in kinks, cusps and loops in the neutral stability curves; points of degeneracy in the R, Ω plane; and branching behaviour on curves which circle a point of degeneracy.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 108 , July 1981 , pp. 101 - 125
Copyright
© 1981 Cambridge University Press

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References

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