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Bifurcations for fluid stirring in circular cavity

Abstract Lagrangian chaos associated with Stokes flows in a circular cavity is addressed in the present study. Two belts arranged on the boundary to be rotated at various speeds are employed to drive this flow motion. The evolutions of several tori are examined when the periods are increased. Then the types of transitions through which the flows change from regular motions to chaotic ones are clearly identified. The routes to chaos for the present studied flows are subject to some successive bifurcations of island‐chains. Those include period‐5, 4, 3, 5, 7 along the direction with increased periods and finally the flows arrive at random motion. The detailed processes of the fluid stirring were numerically visualized and some animations were produced for instructional uses.