The effect of cylinder rotation and blockage ratio on the onset of periodic flows

The steady two-dimensional laminar flow past a stationary cylinder is well known to lose stability to a periodic flow at a supercritical Hopf bifurcation point as the flow rate is increased. It is less well known that the critical flow rate at which the instability occurs can be increased by rotating the cylinder about is own axis, and that at a fixed flow rate the vortex street can be eliminated entirely by sufficiently large rotation. We confine the flow between two parallel walls and report the effect of cylinder rotation on the Reynolds number and frequency at the Hopf bifurcation point. Two new, and somewhat surprising, results are that for stationary cylinders at large blockage ratios, the steady symmetric flow can restabilize above a critical Reynolds number, and that steady asymmetric flows exist.