Motion of a floating sphere pulled by a string and induced flows

Abstract

We study in this article the motion of a floating ball attached to a soft string set in circular motion through its other end. Although simple, the system exhibits rich dynamics that we investigate experimentally and theoretically. At low rotation speeds, we show that the circular trajectory of the ball shrinks when we stir faster, which challenges common intuition based on centrifugal force. For higher rotation rates, the ball is either suddenly attracted toward the center, or is repulsed away from it, depending on the string length. Experimental measurements of the generated flow show that a Magnus force must be taken into account to correctly explain all the observations. In particular, our deformable system allows to measure the ratio of the lift force over the inertial force. Interestingly, the system exhibits strong hysteretic behavior, showing that the ball can robustly trap itself at the center of the flow generated by its past motion. The present experiment also revisits the famous 'tea-leaf paradox', which refers to the unexpected migration of tea leaves toward the center of a tea cup when the latter is mixed with a rigid spoon. The ball attached to the string plays the role of a deformable spoon, and we show that there exists a maximum rotation speed above which the tea-leaves transport brutally stops.