Nature of polygonal structures in flow between rotating disks

Polygonal boundaries between inner and outer parts of rotating flow have been found in several experimental studies of flow between rotating shrouded disks. Such boundaries break axial symmetry of the flow. This analytical study is assigned to understand the physics of such breaking. The presented analysis is based on determination of the curl-free wavy perturbations of steady rotating viscous flows. It is shown that such polygons are the extreme forms of centrifugal waves. These perturbations may transform some streamlines into waves of sharp crests. The computed streamlines obtained polygonal shapes previously observed in experiments.