Chaotic tumbling and steady drifting of bananas in shear flow

The motion of an axisymmetric ellipsoid immersed in a shear flow at zero Reynolds number is simple: the ellipsoid rotates periodically and is advected downstream by the fluid. However, bending the ellipsoid into a banana shape radically changes both its rotational and translational dynamics. The rotation becomes quasiperiodic or chaotic and particles can drift steadily across the streamlines in the gradient and/or the vorticity directions of the shear flow. We explain the origins of drift and the changes in rotational dynamics in terms of the symmetry group of the particle (shared by T-shapes and square pyramids) and the reversibility of Stokes flow, which establish a connection to KAM theory.