Turbulence generated by the oscillatory rotation of a cylindrical container and its occurrence condition

Unsteadiness of the rotation of a container is essential to mix confined fluid without an impeller. As the simplest flow system with an unsteady rotation, we systematically investigate flows in a cylinder whose axial angular velocity is sinusoidal in time. The control parameters of this flow are the Strouhal number, which is the angular frequency of the oscillation normalized by the amplitude of the angular velocity, and the Reynolds number based on the radius of the cylinder and the amplitude of the angular velocity. When the relative velocity is sufficiently large, the boundary layer on the oscillatory wall becomes unstable to form into Görtler vortices. Furthermore, for the case of a high Reynolds number, these vortices collapse and finally generate turbulence filling up in the cylinder. A sufficiently high Strouhal number is necessary to sustain this turbulence. Interestingly, in an early stage of the transition to this developed turbulence, the growing disturbance is localized a pair of distinct column-like structures parallel to the rotational axis, and show a highly two-dimensional and axisymmetric state.