Chaos and Orbital Instability in the Motion of Fluid Particles Due to a Slow Periodic Flow

Chaos and orbital instability in the motion of fluid particles due to the periodic slow rotations of two eccentric cylinders are examined experimentally and numerically for radius ratio 0.24 and eccentricity 0.50. The fluid region between the two cylinders can be divided into the regular region where fluid particles move regularly and the chaotic region where they move chaotically. In the \u27return\u27 experiments, in which the cylinders first rotate alternately by N periods and then rotate in the time-reversal way by N periods, we observe that the deviation for the dye starting from the regular region from its initial position is small even for large N, whereas the deviation for the dye starting from the chaotic region increases rapidly as N increases. This result can be explained as the manifestation of the orbital instability in the chaotic motion. Furthermore, it is shown that the stretching rate of dye due to the alternate rotations of the cylinders strongly depends on its position， and is fairly large near the unstable equilibrium point on the Poincar? section of the particles position after every rotations