 
Summary: Global endwall effects on centrifugally stable flows
Marc Avila,1
Matt Grimes,2
Juan M. Lopez,2
and Francisco Marques1
1
Departament de Física Aplicada, Universitat Politècnica de Catalunya, 08034 Barcelona, Spain
2
Department of Mathematics and Statistics, Arizona State University, Tempe, Arizona 85287, USA
Received 13 May 2008; accepted 4 September 2008; published online 13 October 2008
We investigate the stability of a fluid confined between two cylinders that rotate at same constant
angular speed. In the case of infinite cylinders, or endwalls rotating with the cylinders, the flow is
in solidbody rotation and hence linearly stable for any rotation speed. However, when the endwalls
are stationary, a largescale circulation is driven by radially inward boundary layer flow on the
endwalls. For sufficiently high angular speeds, this circulation becomes unstable to azimuthal
waves. As the lengthtogap aspect ratio of the system is increased, a wealth of instabilities is
revealed. It is particularly interesting that for all these instabilities the associated energy is localized
in the equatorial region, as far from the endwalls as possible. This shows that care must be taken
when assuming localized endwall effects in simplified models. © 2008 American Institute of
Physics. DOI: 10.1063/1.2996326
