Hostname: page-component-7c8c6479df-nwzlb Total loading time: 0 Render date: 2024-03-29T05:41:45.184Z Has data issue: false hasContentIssue false

Survey of instability thresholds of flow between exactly counter-rotating disks

Published online by Cambridge University Press:  12 July 2004

C. NORE
Affiliation:
Université Paris XI, Département de Physique, 91405 Orsay Cedex, France Laboratoire d'Informatique pour la Mécanique et les Sciences de l'Ingénieur, CNRS, BP 133, 91403 Orsay Cedex, France
M. TARTAR
Affiliation:
Laboratoire d'Informatique pour la Mécanique et les Sciences de l'Ingénieur, CNRS, BP 133, 91403 Orsay Cedex, France
O. DAUBE
Affiliation:
LMEE, Université d'Evry Val d'Essonne, 40 rue du Pelvoux, 91020 Evry Cedex, France
L. S. TUCKERMAN
Affiliation:
Laboratoire d'Informatique pour la Mécanique et les Sciences de l'Ingénieur, CNRS, BP 133, 91403 Orsay Cedex, France

Abstract

The three-dimensional linear instability of axisymmetric flow between exactly counter-rotating disks is studied numerically. The dynamics are governed by two parameters, the Reynolds number $Re$ based on cylinder radius and disk rotation speed and the height-to-radius ratio $\Gamma$. The stability analysis performed for $0.5 \,{\le}\, \Gamma \,{\le}\, 3$ shows that non-axisymmetric modes are dominant and stationary and that the critical azimuthal wavenumber is a decreasing function of $\Gamma$. The patterns of the dominant perturbations are analysed and a physical mechanism related to a shear layer instability is discussed. No evidence of complex dynamical behaviour is seen in the neighbourhood of the 1:2 codimension-two point when the $m\,{=}\,2$ threshold precedes that of $m\,{=}\,1$. Axisymmetric instabilities are also calculated; these may be stationary or Hopf bifurcations. Their thresholds are always higher than those of non-axisymmetric modes.

Type
Papers
Copyright
© 2004 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.)