Shear layers in a rotating fluid

Abstract

A homogeneous fluid of viscosity v is confined between two co-axial disks (vertical separation H) which rotate relative to a rotating system (angular velocity Ω). The resulting velocity field is studied for values of the parameter v/2ΩH₂ in the range 1·6 × 10⁻² to 1·8 × 10⁻³. The Rossby number, defined as the ratio of the relative angular velocity of the disks to the angular velocity of the system, ranged from 0·038 to 0·0041. The dependence of the resulting velocity field (interior and boundary-layer flow) on geometrical parameters, imposed surface and bottom velocities, and Ω, is in good agreement with the calculations of Stewartson and Carrier. In particular, when the two disks rotate with the same angular velocity, the width of the vertical shear layer at the edge of the disks is found to be proportional to Ω^{−0·25±0·02}. When the disks rotate in opposite senses, a shear layer in the vertical velocity is observed which transports fluid from one disk to the other and whose width is proportional to Ω^{−0·40±0·10}. The magnitude and shape of the observed vertical velocity is in fair agreement with a numerical integration of the theoretical results.