Fig. 1: (a) Taylor-Couette system with transparent outer cylinder and (b,c) snapshots of the flow for shear Reynolds number 20,000 showing only one-fifteenth of the full cylinder circumference for the cylinder radii 9 and 10. The high-drag state for co-rotating cylinders in (b) consists of a large vortex pair (blue tubes) that organizes the small-scale turbulent vortices (green) into horizontal bands between the large vortices. The second high-drag state for counter-rotating cylinders in (c) is caused by turbulent vortices (green) everywhere close to the cylinder walls.