Global endwall effects on centrifugally stable flows

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 solid-body rotation and hence linearly stable for any rotation speed. However, when the endwalls are stationary, a large-scale 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 length-to-gap 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.