Measurements have been made of the size of the region of secondary flow in a linearly stratified fluid, with Brunt–Va¨isa¨la¨ frequencies in the range of 0.65–3.23 rad/sec, caused by a rotationally oscillating shearing stress. The stress was generated by the surfaces of a disk of radiusr=5.078 cm undergoing torsional oscillations of angular frequency &ohgr;=1.50 rad/sec inside cylindrical boundaries with radii in the range 6.95–10.75 cm. The kinematic viscosity in the vicinity of the disk was approximately constant, &ngr;=1.08 centistokes. Several features of the flow are similar to the secondary flow described by Scranton and Lindberg [Phys. Fluids26, 1198 (1983)] as occurring in annular tank experiments to model geophysical turbulent mixing. For constant Ekman numberEk=&ngr;/&ohgr;r2, the size of the secondary flow region depends on the Brunt–Va¨isa¨la¨ frequency and the boundary radius; an empirical correlation of the data is presented.