On the Bödewadt–Rosenblat flow

Fluid motion induced by the torsional oscillations (of angular velocity bΩcosω T) of an infinite disk in contact with an incompressible viscous rotating (with angular velocity aΩ) fluid of semi-infinite extent is analysed when the amplitude parameter α( = b/a) varies from zero to infinity. Composite solutions valid over the whole of the flow regime and specific expressions for the shearing stress components at the disk and for the axial flow in the far region are obtained for low and high frequencies of torsional oscillations. Using the method of matched asymptotic expansions, we find that the region of the mean flow increases with α and reaches a maximum before settling down to the Rosenblat profile. Series expressions (for α < 1) are deduced for physical quantities of interest when the fluid in the far field and the disk are rotating with different angular velocities (in the same or in the opposite sense), which agree well with the known numerical results.