Flow past a periodically rotating cylinder at subcritical Reynolds numbers

It is well known that in the range of 5 < Re < 47, Föppl vortices are observed in the wake of a fixed cylinder. In this numerical study, we impose periodic rotation on the cylinder to particularly understand its effect on the Föppl vortices and to get an idea of critical values of the parameters for the onset of symmetry-breaking instability, which usually occurs at Re = 47 for the fixed cylinder. We consider a two-dimensional domain with uniform, steady, and incompressible flow at the inlet. The periodic rotation of the cylinder is sinusoidal. We study this problem at four different Reynolds numbers (1, 10, 20, and 40) and for various frequencies and amplitudes of the periodic rotation. We show that as the rotation velocity is increased, the Föppl vortices are observed only momentarily during each cycle of imposed rotation until they disappear after a critical rotation velocity. Instead of Föppl vortices, the imposed rotation induces asymmetric vortices in the wake of the cylinder.