Three-dimensional flow induced by the torsional motion of a cylinder

The flow induced outside a highly flexible cylindrical sheet executing pure torsional motion is studied. The problem is governed by the torsional Reynolds number R= γa²/ν, where γ is the axial rate of rotation, a is the cylinder radius and ν is the fluid kinematic viscosity. An interesting feature of this problem is that the axial pressure gradient of the primary flow induces a weak transverse flow in the meridional plane. The axial component of this motion takes the form of a wall jet. The high Reynolds number asymptotics for the shear stress parameters and the radially entrained flow are presented and compared with full numerical results computed over the large range of Reynolds numbers 10^{- 2} <= R <= 10⁶.