Numerical simulations of the generation of Taylor–Görtler vortices during spin-down to rest in finite-length cylinders

Numerical simulations based on the unsteady Navier–Stokes equations are computed to study confined rotating flows during impulsive spin-down to rest. The focus is on the onset of Taylor–Görtler (TG) vortices generated in the sidewall boundary layer. A stability coefficient Sc is introduced to follow the instant action between centrifugal force and pressure gradient. A new criterion for the prediction of the onset and the onset time of TG vortices is suggested. It is based on the sidewall stability coefficient Sblc, which is an integral of Sc over the region of the sidewall boundary layer. According to this criterion, the TG vortices occur when there is a temporally local increase in Sblc history. The numerical tests show that this criterion is more reliable and accurate than the criterion based on the history of the sidewall torque Ts. It is also shown that the increase in Sblc is particularly sensitive to the dramatic increase in the radial velocity gradient with respect to the axial direction near the midplane where the TG vortices appear first.