Hostname: page-component-848d4c4894-cjp7w Total loading time: 0 Render date: 2024-06-17T11:19:32.604Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Cotton, F. W. 1977 A study of the linear stability problem for viscous incompressible fluids in circular geometries by means of a matrix-eigenvalue approach. Ph.D. dissertation, Stevens Institute of Technology. (University Microfilms International, Ann Arbor, MI. 48106, order no. 77-26,931.)
Cotton, F. W., Salwen, H. & Grosch, C. E. 1973 Bull. Am. Phys. Soc. 20, 1416.
Di Prima, R. C. & Habetler, G. J. 1969 Arch. Rat. Mech. 34, 218–227.
Howard, L. N. & Gupta, A. S. 1962 J. Fluid Mech. 14, 463–476.
Imsl 1975 IMSL Library 2, 5 edn. International Mathematical and Statistical Libraries, Inc., 7500 Bellaire Blvd, Houston, TE. 77036.
Joseph, D. D. & Carmi, S. 1969 Quart. Appl. Math. 16, 575–599.
Lin, C. C. 1955 The Theory of Hydrodynamic Stability. Cambridge University Press.
Mackrodt, P.-A. 1971 Stabilität von Hagen-Poiseuille-Strömungen mit überlagerter starrer Rotation. Mitteilungen aus dem Max-Planck-Institut für Strömungsforschung und der Aerodynamischen Versuchsanstalt (Nr. 55), Göttingen.
Mackrodt, P.-A. 1976 J. Fluid Mech. 73, 153–164.
Maslowe, S. A. 1974 J. Fluid Mech. 64, 307–317.
Parlett, B. N. 1967 The LR and QR algorithms. In Mathematical Methods for Digital Computers, vol. II (ed. A. Ralston & H. S. Wilf). Wiley.
Pedley, T. J. 1968 J. Fluid Mech. 31, 603–607.
Pedley, T. J. 1969 J. Fluid Mech. 35, 97–115.
Salwen, H., Cotton, F. W. & Grosch, C. E. 1980 J. Fluid Mech. 98, 273–284.
Salwen, H. & Grosch, C. E. 1972 J. Fluid Mech. 54, 93–112.
Warren, F. W. 1979 Proc. Roy. Soc. A 368, 225–237.
Wilkinson, J. H. 1965 The Algebraic Eigenvalue Problem. Oxford University Press.