Flow between time-periodically co-rotating cylinders

We consider oscillatory flows between concentric co-rotating cylinders at a ngular velocity Omega(t) = Omega(m) + Omega(o) cos omega t as a prototype t o investigate the competing effects of centrifugal and Coriolis forces on t he flow stability. We first study by flow visualization the effect of the m ean rotation Omega(m) on the centrifugal destabilization due to the tempora l modulation. We show that increasing the mean rotation first destabilizes and then restabilizes the how. The instability of the purely azimuthal basi c flow is then analysed by investigating the dynamics of the axial velocity component of the vortex structures. Velocity measurements performed in the rotating frame of the cylinders using ultrasound Doppler velocimetry show that secondary how appears and disappears several times during a how period . Based on a finite-gap expression for the basic flow, linear stability ana lysis is performed with a quasi-steady approach, providing the times of app earance and disappearance of secondary flow in a cycle as well as the effec t on the instability threshold of the mean rotation. The theoretical and nu merical results are in agreement with experimental results up to intermedia te values of the frequency. Notably, the flow periodically undergoes restab ilization at particular time intervals.