Swirling flow between rotating plates

Abstract

The flow of the classical linearly viscous fluid between two infinite parallel planes rotating with constant (but different) angular velocities about a common axis has received a great deal of attention during the past 60 years (cf. Parter [12]). However, until recently the assumptions which have been employed to study this problem have always led to solutions which are axisymmetric. Recently Berker [3] in his study of the flow between parallel planes rotating with the same constant angular velocities about a common axis exhibited a one parameter family of solutions that are not axisymmetric. In this study we prove that when the planes rotate with different angular velocities about a common axis or distinct axes there is a one parameter family of solutions (for “large” viscosities).